CINXE.COM

<!DOCTYPE html> <html lang="en" dir="ltr"> <head>  <script async src="https://www.googletagmanager.com/gtag/js?id=G-P63WKM1TM1"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-P63WKM1TM1'); </script>  <script type="text/javascript" > (function(m,e,t,r,i,k,a){m[i]=m[i]||function(){(m[i].a=m[i].a||[]).push(arguments)}; m[i].l=1*new Date(); for (var j = 0; j < document.scripts.length; j++) {if (document.scripts[j].src === r) { return; }} k=e.createElement(t),a=e.getElementsByTagName(t)[0],k.async=1,k.src=r,a.parentNode.insertBefore(k,a)}) (window, document, "script", "https://mc.yandex.ru/metrika/tag.js", "ym"); ym(55165297, "init", { clickmap:false, trackLinks:true, accurateTrackBounce:true, webvisor:false }); </script> <noscript><div><img src="https://mc.yandex.ru/watch/55165297" style="position:absolute; left:-9999px;" alt="" /></div></noscript>    <title>Search results for: multilevel graph</title> <meta name="description" content="Search results for: multilevel graph"> <meta name="keywords" content="multilevel graph"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block d-lg-none navbar-toggler ml-auto" type="button" data-toggle="collapse" data-target="#navbarMenu" aria-controls="navbarMenu" aria-expanded="false" aria-label="Toggle navigation"> <span class="navbar-toggler-icon"></span> </button> <div class="w-100"> <div class="d-none d-lg-flex flex-row-reverse"> <form method="get" action="https://waset.org/search" class="form-inline my-2 my-lg-0"> <input class="form-control mr-sm-2" type="search" placeholder="Search Conferences" value="multilevel graph" name="q" aria-label="Search"> <button class="btn btn-light my-2 my-sm-0" type="submit"><i class="fas fa-search"></i></button> </form> </div> <div class="collapse navbar-collapse mt-1" id="navbarMenu"> <ul class="navbar-nav ml-auto align-items-center" id="mainNavMenu"> <li class="nav-item"> <a class="nav-link" href="https://waset.org/conferences" title="Conferences in 2024/2025/2026">Conferences</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/disciplines" title="Disciplines">Disciplines</a> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/committees" rel="nofollow">Committees</a> </li> <li class="nav-item dropdown"> <a class="nav-link dropdown-toggle" href="#" id="navbarDropdownPublications" role="button" data-toggle="dropdown" aria-haspopup="true" aria-expanded="false"> Publications </a> <div class="dropdown-menu" aria-labelledby="navbarDropdownPublications"> <a class="dropdown-item" href="https://publications.waset.org/abstracts">Abstracts</a> <a class="dropdown-item" href="https://publications.waset.org">Periodicals</a> <a class="dropdown-item" href="https://publications.waset.org/archive">Archive</a> </div> </li> <li class="nav-item"> <a class="nav-link" href="https://waset.org/page/support" title="Support">Support</a> </li> </ul> </div> </div> </nav> </div> </header> <main> <div class="container mt-4"> <div class="row"> <div class="col-md-9 mx-auto"> <form method="get" action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="multilevel graph"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 616</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: multilevel graph</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">616</span> Topological Indices of Some Graph Operations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=U.%20Mary">U. Mary </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let be a graph with a finite, nonempty set of objects called vertices together with a set of unordered pairs of distinct vertices of called edges. The vertex set is denoted by and the edge set by. Given two graphs and the wiener index of, wiener index for the splitting graph of a graph, the first Zagreb index of and its splitting graph, the 3-steiner wiener index of, the 3-steiner wiener index of a special graph are explored in this paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complementary%20prism%20graph" title="complementary prism graph">complementary prism graph</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20Zagreb%20index" title=" first Zagreb index"> first Zagreb index</a>, <a href="https://publications.waset.org/abstracts/search?q=neighborhood%20corona%20graph" title=" neighborhood corona graph"> neighborhood corona graph</a>, <a href="https://publications.waset.org/abstracts/search?q=steiner%20distance" title=" steiner distance"> steiner distance</a>, <a href="https://publications.waset.org/abstracts/search?q=splitting%20graph" title=" splitting graph"> splitting graph</a>, <a href="https://publications.waset.org/abstracts/search?q=steiner%20wiener%20index" title=" steiner wiener index"> steiner wiener index</a>, <a href="https://publications.waset.org/abstracts/search?q=wiener%20index" title=" wiener index"> wiener index</a> </p> <a href="https://publications.waset.org/abstracts/16774/topological-indices-of-some-graph-operations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16774.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">570</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">615</span> Survey Paper on Graph Coloring Problem and Its Application</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Prateek%20Chharia">Prateek Chharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Biswa%20Bhusan%20Ghosh"> Biswa Bhusan Ghosh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph coloring is one of the prominent concepts in graph coloring. It can be defined as a coloring of the various regions of the graph such that all the constraints are fulfilled. In this paper various graphs coloring approaches like greedy coloring, Heuristic search for maximum independent set and graph coloring using edge table is described. Graph coloring can be used in various real time applications like student time tabling generation, Sudoku as a graph coloring problem, GSM phone network. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20coloring" title="graph coloring">graph coloring</a>, <a href="https://publications.waset.org/abstracts/search?q=greedy%20coloring" title=" greedy coloring"> greedy coloring</a>, <a href="https://publications.waset.org/abstracts/search?q=heuristic%20search" title=" heuristic search"> heuristic search</a>, <a href="https://publications.waset.org/abstracts/search?q=edge%20table" title=" edge table"> edge table</a>, <a href="https://publications.waset.org/abstracts/search?q=sudoku%20as%20a%20graph%20coloring%20problem" title=" sudoku as a graph coloring problem"> sudoku as a graph coloring problem</a> </p> <a href="https://publications.waset.org/abstracts/19691/survey-paper-on-graph-coloring-problem-and-its-application" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19691.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">539</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">614</span> A New Graph Theoretic Problem with Ample Practical Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mehmet%20Hakan%20Karaata">Mehmet Hakan Karaata</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=algorithm" title="algorithm">algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=cycle" title=" cycle"> cycle</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20algorithm" title=" graph algorithm"> graph algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20theory" title=" graph theory"> graph theory</a>, <a href="https://publications.waset.org/abstracts/search?q=network%20structuring" title=" network structuring"> network structuring</a> </p> <a href="https://publications.waset.org/abstracts/67285/a-new-graph-theoretic-problem-with-ample-practical-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67285.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">386</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">613</span> Complete Tripartite Graphs with Spanning Maximal Planar Subgraphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Severino%20Gervacio">Severino Gervacio</a>, <a href="https://publications.waset.org/abstracts/search?q=Velimor%20Almonte"> Velimor Almonte</a>, <a href="https://publications.waset.org/abstracts/search?q=Emmanuel%20Natalio"> Emmanuel Natalio</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A simple graph is planar if it there is a way of drawing it in the plane without edge crossings. A planar graph which is not a proper spanning subgraph of another planar graph is a maximal planar graph. We prove that for complete tripartite graphs of order at most 9, the only ones that contain a spanning maximal planar subgraph are K1,1,1, K2,2,2, K2,3,3, and K3,3,3. The main result gives a necessary and sufficient condition for the complete tripartite graph Kx,y,z to contain a spanning maximal planar subgraph. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=complete%20tripartite%20graph" title="complete tripartite graph">complete tripartite graph</a>, <a href="https://publications.waset.org/abstracts/search?q=graph" title=" graph"> graph</a>, <a href="https://publications.waset.org/abstracts/search?q=maximal%20planar%20graph" title=" maximal planar graph"> maximal planar graph</a>, <a href="https://publications.waset.org/abstracts/search?q=planar%20graph" title=" planar graph"> planar graph</a>, <a href="https://publications.waset.org/abstracts/search?q=subgraph" title=" subgraph"> subgraph</a> </p> <a href="https://publications.waset.org/abstracts/59157/complete-tripartite-graphs-with-spanning-maximal-planar-subgraphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59157.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">381</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">612</span> Efficient Filtering of Graph Based Data Using Graph Partitioning</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nileshkumar%20Vaishnav">Nileshkumar Vaishnav</a>, <a href="https://publications.waset.org/abstracts/search?q=Aditya%20Tatu"> Aditya Tatu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An algebraic framework for processing graph signals axiomatically designates the graph adjacency matrix as the shift operator. In this setup, we often encounter a problem wherein we know the filtered output and the filter coefficients, and need to find out the input graph signal. Solution to this problem using direct approach requires O(N3) operations, where N is the number of vertices in graph. In this paper, we adapt the spectral graph partitioning method for partitioning of graphs and use it to reduce the computational cost of the filtering problem. We use the example of denoising of the temperature data to illustrate the efficacy of the approach. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20signal%20processing" title="graph signal processing">graph signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20partitioning" title=" graph partitioning"> graph partitioning</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20filtering%20on%20graphs" title=" inverse filtering on graphs"> inverse filtering on graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=algebraic%20signal%20processing" title=" algebraic signal processing"> algebraic signal processing</a> </p> <a href="https://publications.waset.org/abstracts/59397/efficient-filtering-of-graph-based-data-using-graph-partitioning" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59397.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">311</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">611</span> Improvement a Lower Bound of Energy for Some Family of Graphs, Related to Determinant of Adjacency Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saieed%20%20Akbari">Saieed Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Yousef%20Bagheri"> Yousef Bagheri</a>, <a href="https://publications.waset.org/abstracts/search?q=Amir%20Hossein%20Ghodrati"> Amir Hossein Ghodrati</a>, <a href="https://publications.waset.org/abstracts/search?q=Sima%20Saadat%20Akhtar"> Sima Saadat Akhtar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let G be a simple graph with the vertex set V (G) and with the adjacency matrix A (G). The energy E (G) of G is defined to be the sum of the absolute values of all eigenvalues of A (G). Also let n and m be number of edges and vertices of the graph respectively. A regular graph is a graph where each vertex has the same number of neighbours. Given a graph G, its line graph L(G) is a graph such that each vertex of L(G) represents an edge of G; and two vertices of L(G) are adjacent if and only if their corresponding edges share a common endpoint in G. In this paper we show that for every regular graphs and also for every line graphs such that (G) 3 we have, E(G) 2nm + n 1. Also at the other part of the paper we prove that 2 (G) E(G) for an arbitrary graph G. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenvalues" title="eigenvalues">eigenvalues</a>, <a href="https://publications.waset.org/abstracts/search?q=energy" title=" energy"> energy</a>, <a href="https://publications.waset.org/abstracts/search?q=line%20graphs" title=" line graphs"> line graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=matching%20number" title=" matching number"> matching number</a> </p> <a href="https://publications.waset.org/abstracts/99652/improvement-a-lower-bound-of-energy-for-some-family-of-graphs-related-to-determinant-of-adjacency-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/99652.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">232</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">610</span> Graph Similarity: Algebraic Model and Its Application to Nonuniform Signal Processing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nileshkumar%20Vishnav">Nileshkumar Vishnav</a>, <a href="https://publications.waset.org/abstracts/search?q=Aditya%20Tatu"> Aditya Tatu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A recent approach of representing graph signals and graph filters as polynomials is useful for graph signal processing. In this approach, the adjacency matrix plays pivotal role; instead of the more common approach involving graph-Laplacian. In this work, we follow the adjacency matrix based approach and corresponding algebraic signal model. We further expand the theory and introduce the concept of similarity of two graphs. The similarity of graphs is useful in that key properties (such as filter-response, algebra related to graph) get transferred from one graph to another. We demonstrate potential applications of the relation between two similar graphs, such as nonuniform filter design, DTMF detection and signal reconstruction. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20signal%20processing" title="graph signal processing">graph signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=algebraic%20signal%20processing" title=" algebraic signal processing"> algebraic signal processing</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20similarity" title=" graph similarity"> graph similarity</a>, <a href="https://publications.waset.org/abstracts/search?q=isospectral%20graphs" title=" isospectral graphs"> isospectral graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=nonuniform%20signal%20processing" title=" nonuniform signal processing"> nonuniform signal processing</a> </p> <a href="https://publications.waset.org/abstracts/59404/graph-similarity-algebraic-model-and-its-application-to-nonuniform-signal-processing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59404.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">352</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">609</span> Metric Dimension on Line Graph of Honeycomb Networks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Hussain">M. Hussain</a>, <a href="https://publications.waset.org/abstracts/search?q=Aqsa%20Farooq"> Aqsa Farooq</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let G = (V,E) be a connected graph and distance between any two vertices a and b in G is a−b geodesic and is denoted by d(a, b). A set of vertices W resolves a graph G if each vertex is uniquely determined by its vector of distances to the vertices in W. A metric dimension of G is the minimum cardinality of a resolving set of G. In this paper line graph of honeycomb network has been derived and then we calculated the metric dimension on line graph of honeycomb network. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Resolving%20set" title="Resolving set">Resolving set</a>, <a href="https://publications.waset.org/abstracts/search?q=Metric%20dimension" title=" Metric dimension"> Metric dimension</a>, <a href="https://publications.waset.org/abstracts/search?q=Honeycomb%20network" title=" Honeycomb network"> Honeycomb network</a>, <a href="https://publications.waset.org/abstracts/search?q=Line%20graph" title=" Line graph"> Line graph</a> </p> <a href="https://publications.waset.org/abstracts/101558/metric-dimension-on-line-graph-of-honeycomb-networks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/101558.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">200</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">608</span> Speedup Breadth-First Search by Graph Ordering</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Qiuyi%20Lyu">Qiuyi Lyu</a>, <a href="https://publications.waset.org/abstracts/search?q=Bin%20Gong"> Bin Gong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Breadth-First Search(BFS) is a core graph algorithm that is widely used for graph analysis. As it is frequently used in many graph applications, improve the BFS performance is essential. In this paper, we present a graph ordering method that could reorder the graph nodes to achieve better data locality, thus, improving the BFS performance. Our method is based on an observation that the sibling relationships will dominate the cache access pattern during the BFS traversal. Therefore, we propose a frequency-based model to construct the graph order. First, we optimize the graph order according to the nodes’ visit frequency. Nodes with high visit frequency will be processed in priority. Second, we try to maximize the child nodes overlap layer by layer. As it is proved to be NP-hard, we propose a heuristic method that could greatly reduce the preprocessing overheads. We conduct extensive experiments on 16 real-world datasets. The result shows that our method could achieve comparable performance with the state-of-the-art methods while the graph ordering overheads are only about 1/15. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=breadth-first%20search" title="breadth-first search">breadth-first search</a>, <a href="https://publications.waset.org/abstracts/search?q=BFS" title=" BFS"> BFS</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20ordering" title=" graph ordering"> graph ordering</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20algorithm" title=" graph algorithm"> graph algorithm</a> </p> <a href="https://publications.waset.org/abstracts/136790/speedup-breadth-first-search-by-graph-ordering" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/136790.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">138</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">607</span> A Study of Families of Bistar and Corona Product of Graph: Reverse Topological Indices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gowtham%20Kalkere%20Jayanna">Gowtham Kalkere Jayanna</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamad%20Nazri%20Husin"> Mohamad Nazri Husin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph theory, chemistry, and technology are all combined in cheminformatics. The structure and physiochemical properties of organic substances are linked using some useful graph invariants and the corresponding molecular graph. In this paper, we study specific reverse topological indices such as the reverse sum-connectivity index, the reverse Zagreb index, the reverse arithmetic-geometric, and the geometric-arithmetic, the reverse Sombor, the reverse Nirmala indices for the bistar graphs B (n: m) and the corona product Kₘ∘Kₙ', where Kₙ' Represent the complement of a complete graph Kₙ. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=reverse%20topological%20indices" title="reverse topological indices">reverse topological indices</a>, <a href="https://publications.waset.org/abstracts/search?q=bistar%20graph" title=" bistar graph"> bistar graph</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20corona%20product" title=" the corona product"> the corona product</a>, <a href="https://publications.waset.org/abstracts/search?q=graph" title=" graph"> graph</a> </p> <a href="https://publications.waset.org/abstracts/166540/a-study-of-families-of-bistar-and-corona-product-of-graph-reverse-topological-indices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/166540.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">97</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">606</span> On the Zeros of the Degree Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20R.%20Nayaka">S. R. Nayaka</a>, <a href="https://publications.waset.org/abstracts/search?q=Putta%20Swamy"> Putta Swamy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Graph polynomial is one of the algebraic representations of the Graph. The degree polynomial is one of the simple algebraic representations of graphs. The degree polynomial of a graph G of order n is the polynomial Deg(G, x) with the coefficients deg(G,i) where deg(G,i) denotes the number of vertices of degree i in G. In this article, we investigate the behavior of the roots of some families of Graphs in the complex field. We investigate for the graphs having only integral roots. Further, we characterize the graphs having single roots or having real roots and behavior of the polynomial at the particular value is also obtained. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=degree%20polynomial" title="degree polynomial">degree polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=regular%20graph" title=" regular graph"> regular graph</a>, <a href="https://publications.waset.org/abstracts/search?q=minimum%20and%20maximum%20degree" title=" minimum and maximum degree"> minimum and maximum degree</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20operations" title=" graph operations"> graph operations</a> </p> <a href="https://publications.waset.org/abstracts/56602/on-the-zeros-of-the-degree-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56602.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">249</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">605</span> From Convexity in Graphs to Polynomial Rings</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ladznar%20S.%20Laja">Ladznar S. Laja</a>, <a href="https://publications.waset.org/abstracts/search?q=Rosalio%20G.%20Artes"> Rosalio G. Artes</a>, <a href="https://publications.waset.org/abstracts/search?q=Jr."> Jr.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper introduced a graph polynomial relating convexity concepts. A graph polynomial is a polynomial representing a graph given some parameters. On the other hand, a subgraph H of a graph G is said to be convex in G if for every pair of vertices in H, every shortest path with these end-vertices lies entirely in H. We define the convex subgraph polynomial of a graph G to be the generating function of the sequence of the numbers of convex subgraphs of G of cardinalities ranging from zero to the order of G. This graph polynomial is monic since G itself is convex. The convex index which counts the number of convex subgraphs of G of all orders is just the evaluation of this polynomial at 1. Relationships relating algebraic properties of convex subgraphs polynomial with graph theoretic concepts are established. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=convex%20subgraph" title="convex subgraph">convex subgraph</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20index" title=" convex index"> convex index</a>, <a href="https://publications.waset.org/abstracts/search?q=generating%20function" title=" generating function"> generating function</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20ring" title=" polynomial ring"> polynomial ring</a> </p> <a href="https://publications.waset.org/abstracts/9019/from-convexity-in-graphs-to-polynomial-rings" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9019.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">604</span> Hybrid PWM Techniques for the Reduction of Switching Losses and Voltage Harmonics in Cascaded Multilevel Inverters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Venkata%20Reddy%20Kota">Venkata Reddy Kota</a> </p> <p class="card-text"><strong>Abstract:</strong></p> These days, the industrial trend is moving away from heavy and bulky passive components to power converter systems that use more and more semiconductor elements. Also, it is difficult to connect the traditional converters to the high and medium voltage. For these reasons, a new family of multilevel inverters has appeared as a solution for working with higher voltage levels. Different modulation topologies like Sinusoidal Pulse Width Modulation (SPWM), Selective Harmonic Elimination Pulse Width Modulation (SHE-PWM) are available for multilevel inverters. In this work, different hybrid modulation techniques which are combination of fundamental frequency modulation and multilevel sinusoidal-modulation are compared. The main characteristic of these modulations are reduction of switching losses with good harmonic performance and balanced power loss dissipation among the device. The proposed hybrid modulation schemes are developed and simulated in Matlab/Simulink for cascaded H-bridge inverter. The results validate the applicability of the proposed schemes for cascaded multilevel inverter. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20PWM%20techniques" title="hybrid PWM techniques">hybrid PWM techniques</a>, <a href="https://publications.waset.org/abstracts/search?q=cascaded%20multilevel%20inverters" title=" cascaded multilevel inverters"> cascaded multilevel inverters</a>, <a href="https://publications.waset.org/abstracts/search?q=switching%20loss%20minimization" title=" switching loss minimization"> switching loss minimization</a> </p> <a href="https://publications.waset.org/abstracts/12634/hybrid-pwm-techniques-for-the-reduction-of-switching-losses-and-voltage-harmonics-in-cascaded-multilevel-inverters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12634.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">616</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">603</span> An Application of Graph Theory to The Electrical Circuit Using Matrix Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Samai%27la%20Abdullahi">Samai'la Abdullahi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A graph is a pair of two set and so that a graph is a pictorial representation of a system using two basic element nodes and edges. A node is represented by a circle (either hallo shade) and edge is represented by a line segment connecting two nodes together. In this paper, we present a circuit network in the concept of graph theory application and also circuit models of graph are represented in logical connection method were we formulate matrix method of adjacency and incidence of matrix and application of truth table. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=euler%20circuit%20and%20path" title="euler circuit and path">euler circuit and path</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20representation%20of%20circuit%20networks" title=" graph representation of circuit networks"> graph representation of circuit networks</a>, <a href="https://publications.waset.org/abstracts/search?q=representation%20of%20graph%20models" title=" representation of graph models"> representation of graph models</a>, <a href="https://publications.waset.org/abstracts/search?q=representation%20of%20circuit%20network%20using%20logical%20truth%20table" title=" representation of circuit network using logical truth table"> representation of circuit network using logical truth table</a> </p> <a href="https://publications.waset.org/abstracts/32358/an-application-of-graph-theory-to-the-electrical-circuit-using-matrix-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32358.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">561</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">602</span> Building 1-Well-Covered Graphs by Corona, Join, and Rooted Product of Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Vadim%20E.%20Levit">Vadim E. Levit</a>, <a href="https://publications.waset.org/abstracts/search?q=Eugen%20Mandrescu"> Eugen Mandrescu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A graph is well-covered if all its maximal independent sets are of the same size. A well-covered graph is 1-well-covered if deletion of every vertex of the graph leaves it well-covered. It is known that a graph without isolated vertices is 1-well-covered if and only if every two disjoint independent sets are included in two disjoint maximum independent sets. Well-covered graphs are related to combinatorial commutative algebra (e.g., every Cohen-Macaulay graph is well-covered, while each Gorenstein graph without isolated vertices is 1-well-covered). Our intent is to construct several infinite families of 1-well-covered graphs using the following known graph operations: corona, join, and rooted product of graphs. Adopting some known techniques used to advantage for well-covered graphs, one can prove that: if the graph G has no isolated vertices, then the corona of G and H is 1-well-covered if and only if H is a complete graph of order two at least; the join of the graphs G and H is 1-well-covered if and only if G and H have the same independence number and both are 1-well-covered; if H satisfies the property that every three pairwise disjoint independent sets are included in three pairwise disjoint maximum independent sets, then the rooted product of G and H is 1-well-covered, for every graph G. These findings show not only how to generate some more families of 1-well-covered graphs, but also that, to this aim, sometimes, one may use graphs that are not necessarily 1-well-covered. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=maximum%20independent%20set" title="maximum independent set">maximum independent set</a>, <a href="https://publications.waset.org/abstracts/search?q=corona" title=" corona"> corona</a>, <a href="https://publications.waset.org/abstracts/search?q=concatenation" title=" concatenation"> concatenation</a>, <a href="https://publications.waset.org/abstracts/search?q=join" title=" join"> join</a>, <a href="https://publications.waset.org/abstracts/search?q=well-covered%20graph" title=" well-covered graph"> well-covered graph</a> </p> <a href="https://publications.waset.org/abstracts/86859/building-1-well-covered-graphs-by-corona-join-and-rooted-product-of-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86859.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">208</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">601</span> Nullity of t-Tupple Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khidir%20R.%20Sharaf">Khidir R. Sharaf</a>, <a href="https://publications.waset.org/abstracts/search?q=Didar%20A.%20Ali"> Didar A. Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The nullity η (G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f (w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced sub-graph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the end vertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived and determined for some special types of graphs. Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20theory" title="graph theory">graph theory</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20spectra" title=" graph spectra"> graph spectra</a>, <a href="https://publications.waset.org/abstracts/search?q=nullity%20of%20graphs" title=" nullity of graphs"> nullity of graphs</a>, <a href="https://publications.waset.org/abstracts/search?q=statistic" title=" statistic"> statistic</a> </p> <a href="https://publications.waset.org/abstracts/4759/nullity-of-t-tupple-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4759.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">239</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">600</span> Existence and Construction of Maximal Rectangular Duals</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Krishnendra%20Shekhawat">Krishnendra Shekhawat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Given a graph G = (V, E), a rectangular dual of G represents the vertices of G by a set of interior-disjoint rectangles such that two rectangles touch if and only if there is an edge between the two corresponding vertices in G. Rectangular duals do not exist for every graph, so we can define maximal rectangular duals. A maximal rectangular dual is a rectangular dual of a graph G such that there exists no graph G ′ with a rectangular dual where G is a subgraph of G ′. In this paper, we enumerate all maximal rectangular duals (or, to be precise, the corresponding planar graphs) up to six nodes and presents a necessary condition for the existence of a rectangular dual. This work allegedly has applications in integrated circuit design and architectural floor plans. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adjacency" title="adjacency">adjacency</a>, <a href="https://publications.waset.org/abstracts/search?q=degree%20sequence" title=" degree sequence"> degree sequence</a>, <a href="https://publications.waset.org/abstracts/search?q=dual%20graph" title=" dual graph"> dual graph</a>, <a href="https://publications.waset.org/abstracts/search?q=rectangular%20dual" title=" rectangular dual"> rectangular dual</a> </p> <a href="https://publications.waset.org/abstracts/62583/existence-and-construction-of-maximal-rectangular-duals" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/62583.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">266</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">599</span> Characterising Stable Model by Extended Labelled Dependency Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Asraful%20Islam">Asraful Islam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Extended dependency graph (EDG) is a state-of-the-art isomorphic graph to represent normal logic programs (NLPs) that can characterize the consistency of NLPs by graph analysis. To construct the vertices and arcs of an EDG, additional renaming atoms and rules besides those the given program provides are used, resulting in higher space complexity compared to the corresponding traditional dependency graph (TDG). In this article, we propose an extended labeled dependency graph (ELDG) to represent an NLP that shares an equal number of nodes and arcs with TDG and prove that it is isomorphic to the domain program. The number of nodes and arcs used in the underlying dependency graphs are formulated to compare the space complexity. Results show that ELDG uses less memory to store nodes, arcs, and cycles compared to EDG. To exhibit the desirability of ELDG, firstly, the stable models of the kernel form of NLP are characterized by the admissible coloring of ELDG; secondly, a relation of the stable models of a kernel program with the handles of the minimal, odd cycles appearing in the corresponding ELDG has been established; thirdly, to our best knowledge, for the first time an inverse transformation from a dependency graph to the representing NLP w.r.t. ELDG has been defined that enables transferring analytical results from the graph to the program straightforwardly. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=normal%20logic%20program" title="normal logic program">normal logic program</a>, <a href="https://publications.waset.org/abstracts/search?q=isomorphism%20of%20graph" title=" isomorphism of graph"> isomorphism of graph</a>, <a href="https://publications.waset.org/abstracts/search?q=extended%20labelled%20dependency%20graph" title=" extended labelled dependency graph"> extended labelled dependency graph</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20graph%20transforma-tion" title=" inverse graph transforma-tion"> inverse graph transforma-tion</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20colouring" title=" graph colouring"> graph colouring</a> </p> <a href="https://publications.waset.org/abstracts/137606/characterising-stable-model-by-extended-labelled-dependency-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/137606.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">213</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">598</span> Implementation of a Novel Modified Multilevel Inverter Topology for Grid Connected PV System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Dhivya%20Balakrishnan">Dhivya Balakrishnan</a>, <a href="https://publications.waset.org/abstracts/search?q=Dhamodharan%20Shanmugam"> Dhamodharan Shanmugam</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Multilevel converters offer high power capability, associated with lower output harmonics and lower commutation losses. Their main disadvantage is their complexity requiring a great number of power devices and passive components, and a rather complex control circuitry. This paper proposes a single-phase seven-level inverter for grid connected PV systems, With a novel pulse width-modulated (PWM) control scheme. Three reference signals that are identical to each other with an offset that is equivalent to the amplitude of the triangular carrier signal were used to generate the PWM signals. The inverter is capable of producing seven levels of output-voltage levels from the dc supply voltage. This paper proposes a new multilevel inverter topology using an H-bridge output stage with two bidirectional auxiliary switches. The new topology produces a significant reduction in the number of power devices and capacitors required to implement a multilevel output using the asymmetric cascade configuration. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymmetric%20cascade%20configuration" title="asymmetric cascade configuration">asymmetric cascade configuration</a>, <a href="https://publications.waset.org/abstracts/search?q=H-Bridge" title=" H-Bridge"> H-Bridge</a>, <a href="https://publications.waset.org/abstracts/search?q=multilevel%20inverter" title=" multilevel inverter"> multilevel inverter</a>, <a href="https://publications.waset.org/abstracts/search?q=Pulse%20Width%20Modulation%20%28PWM%29" title=" Pulse Width Modulation (PWM)"> Pulse Width Modulation (PWM)</a> </p> <a href="https://publications.waset.org/abstracts/1763/implementation-of-a-novel-modified-multilevel-inverter-topology-for-grid-connected-pv-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1763.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">357</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">597</span> Introduction to Paired Domination Polynomial of a Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Puttaswamy">Puttaswamy</a>, <a href="https://publications.waset.org/abstracts/search?q=Anwar%20Alwardi"> Anwar Alwardi</a>, <a href="https://publications.waset.org/abstracts/search?q=Nayaka%20S.%20R."> Nayaka S. R.</a> </p> <p class="card-text"><strong>Abstract:</strong></p> One of the algebraic representation of a graph is the graph polynomial. In this article, we introduce the paired-domination polynomial of a graph G. The paired-domination polynomial of a graph G of order n is the polynomial Dp(G, x) with the coefficients dp(G, i) where dp(G, i) denotes the number of paired dominating sets of G of cardinality i and γpd(G) denotes the paired-domination number of G. We obtain some properties of Dp(G, x) and its coefficients. Further, we compute this polynomial for some families of standard graphs. Further, we obtain some characterization for some specific graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=domination%20polynomial" title="domination polynomial">domination polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20dominating%20set" title=" paired dominating set"> paired dominating set</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20number" title=" paired domination number"> paired domination number</a>, <a href="https://publications.waset.org/abstracts/search?q=paired%20domination%20polynomial" title=" paired domination polynomial"> paired domination polynomial</a> </p> <a href="https://publications.waset.org/abstracts/52964/introduction-to-paired-domination-polynomial-of-a-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52964.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">232</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">596</span> Eccentric Connectivity Index, First and Second Zagreb Indices of Corona Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Kulandai%20Therese">A. Kulandai Therese</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The eccentric connectivity index based on degree and eccentricity of the vertices of a graph is a widely used graph invariant in mathematics.In this paper, we present the explicit eccentric connectivity index, first and second Zagreb indices for a Corona graph and sub division-related corona graphs. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=corona%20graph" title="corona graph">corona graph</a>, <a href="https://publications.waset.org/abstracts/search?q=degree" title=" degree"> degree</a>, <a href="https://publications.waset.org/abstracts/search?q=eccentricity" title=" eccentricity"> eccentricity</a>, <a href="https://publications.waset.org/abstracts/search?q=eccentric%20connectivity%20index" title=" eccentric connectivity index"> eccentric connectivity index</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20zagreb%20index" title=" first zagreb index"> first zagreb index</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20zagreb%20index" title=" second zagreb index"> second zagreb index</a>, <a href="https://publications.waset.org/abstracts/search?q=subdivision%20graphs" title=" subdivision graphs"> subdivision graphs</a> </p> <a href="https://publications.waset.org/abstracts/16768/eccentric-connectivity-index-first-and-second-zagreb-indices-of-corona-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16768.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">338</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">595</span> 2D Structured Non-Cyclic Fuzzy Graphs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20Pathinathan">T. Pathinathan</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Peter"> M. Peter</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy graphs incorporate concepts from graph theory with fuzzy principles. In this paper, we make a study on the properties of fuzzy graphs which are non-cyclic and are of two-dimensional in structure. In particular, this paper presents 2D structure or the structure of double layer for a non-cyclic fuzzy graph whose underlying crisp graph is non-cyclic. In any graph structure, introducing 2D structure may lead to an inherent cycle. We propose relevant conditions for 2D structured non-cyclic fuzzy graphs. These conditions are extended even to fuzzy graphs of the 3D structure. General theoretical properties that are studied for any fuzzy graph are verified to 2D structured or double layered fuzzy graphs. Concepts like Order, Degree, Strong and Size for a fuzzy graph are studied for 2D structured or double layered non-cyclic fuzzy graphs. Using different types of fuzzy graphs, the proposed concepts relating to 2D structured fuzzy graphs are verified. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=double%20layered%20fuzzy%20graph" title="double layered fuzzy graph">double layered fuzzy graph</a>, <a href="https://publications.waset.org/abstracts/search?q=double%20layered%20non%E2%80%93cyclic%20fuzzy%20graph" title=" double layered non–cyclic fuzzy graph"> double layered non–cyclic fuzzy graph</a>, <a href="https://publications.waset.org/abstracts/search?q=order" title=" order"> order</a>, <a href="https://publications.waset.org/abstracts/search?q=degree%20and%20size" title=" degree and size"> degree and size</a> </p> <a href="https://publications.waset.org/abstracts/80562/2d-structured-non-cyclic-fuzzy-graphs" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80562.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">400</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">594</span> Minimization of Switching Losses in Cascaded Multilevel Inverters Using Efficient Sequential Switching Hybrid-Modulation Techniques</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=P.%20Satish%20Kumar">P. Satish Kumar</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20Ramakrishna"> K. Ramakrishna</a>, <a href="https://publications.waset.org/abstracts/search?q=Ch.%20Lokeshwar%20Reddy"> Ch. Lokeshwar Reddy</a>, <a href="https://publications.waset.org/abstracts/search?q=G.%20Sridhar"> G. Sridhar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents two different sequential switching hybrid-modulation strategies and implemented for cascaded multilevel inverters. Hybrid modulation strategies represent the combinations of Fundamental-Frequency Pulse Width Modulation (FFPWM) and Multilevel Sinusoidal-Modulation (MSPWM) strategies, and are designed for performance of the well-known Alternative Phase Opposition Disposition (APOD), Phase Shifted Carrier (PSC). The main characteristics of these modulations are the reduction of switching losses with good harmonic performance, balanced power loss dissipation among the devices with in a cell, and among the series-connected cells. The feasibility of these modulations is verified through spectral analysis, power loss analysis and simulation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cascaded%20multilevel%20inverters" title="cascaded multilevel inverters">cascaded multilevel inverters</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20modulation" title=" hybrid modulation"> hybrid modulation</a>, <a href="https://publications.waset.org/abstracts/search?q=power%20loss%20analysis" title=" power loss analysis"> power loss analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=pulse%20width%20modulation" title=" pulse width modulation"> pulse width modulation</a> </p> <a href="https://publications.waset.org/abstracts/7094/minimization-of-switching-losses-in-cascaded-multilevel-inverters-using-efficient-sequential-switching-hybrid-modulation-techniques" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7094.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">537</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">593</span> Multi-Stream Graph Attention Network for Recommendation with Knowledge Graph</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhifei%20Hu">Zhifei Hu</a>, <a href="https://publications.waset.org/abstracts/search?q=Feng%20Xia"> Feng Xia</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In recent years, Graph neural network has been widely used in knowledge graph recommendation. The existing recommendation methods based on graph neural network extract information from knowledge graph through entity and relation, which may not be efficient in the way of information extraction. In order to better propose useful entity information for the current recommendation task in the knowledge graph, we propose an end-to-end Neural network Model based on multi-stream graph attentional Mechanism (MSGAT), which can effectively integrate the knowledge graph into the recommendation system by evaluating the importance of entities from both users and items. Specifically, we use the attention mechanism from the user's perspective to distil the domain nodes information of the predicted item in the knowledge graph, to enhance the user's information on items, and generate the feature representation of the predicted item. Due to user history, click items can reflect the user's interest distribution, we propose a multi-stream attention mechanism, based on the user's preference for entities and relationships, and the similarity between items to be predicted and entities, aggregate user history click item's neighborhood entity information in the knowledge graph and generate the user's feature representation. We evaluate our model on three real recommendation datasets: Movielens-1M (ML-1M), LFM-1B 2015 (LFM-1B), and Amazon-Book (AZ-book). Experimental results show that compared with the most advanced models, our proposed model can better capture the entity information in the knowledge graph, which proves the validity and accuracy of the model. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20attention%20network" title="graph attention network">graph attention network</a>, <a href="https://publications.waset.org/abstracts/search?q=knowledge%20graph" title=" knowledge graph"> knowledge graph</a>, <a href="https://publications.waset.org/abstracts/search?q=recommendation" title=" recommendation"> recommendation</a>, <a href="https://publications.waset.org/abstracts/search?q=information%20propagation" title=" information propagation"> information propagation</a> </p> <a href="https://publications.waset.org/abstracts/150710/multi-stream-graph-attention-network-for-recommendation-with-knowledge-graph" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/150710.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">117</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">592</span> Ant Colony Optimization Control for Multilevel STATCOM</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20T%C3%A9djini">H. Tédjini</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20Meslem"> Y. Meslem</a>, <a href="https://publications.waset.org/abstracts/search?q=B.%20Guesbaoui"> B. Guesbaoui</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Safa"> A. Safa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Flexible AC Transmission Systems (FACTS) are potentially becoming more flexible and more economical local controllers in the power system; and because of the high MVA ratings, it would be expensive to provide independent, equal, regulated DC voltage sources to power the multilevel converters which are presently proposed for STATCOMs. DC voltage sources can be derived from the DC link capacitances which are charged by the rectified ac power. In this paper a new stronger control combined of nonlinear control based Lyapunov’s theorem and Ant Colony Algorithm (ACA) to maintain stability of multilevel STATCOM and the utility. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Static%20Compensator%20%28STATCOM%29" title="Static Compensator (STATCOM)">Static Compensator (STATCOM)</a>, <a href="https://publications.waset.org/abstracts/search?q=ant%20colony%20optimization%20%28ACO%29" title=" ant colony optimization (ACO)"> ant colony optimization (ACO)</a>, <a href="https://publications.waset.org/abstracts/search?q=lyapunov%20control%20theory" title=" lyapunov control theory"> lyapunov control theory</a>, <a href="https://publications.waset.org/abstracts/search?q=Decoupled%20power%20control" title=" Decoupled power control"> Decoupled power control</a>, <a href="https://publications.waset.org/abstracts/search?q=neutral%20point%20clamped%20%28NPC%29" title=" neutral point clamped (NPC)"> neutral point clamped (NPC)</a> </p> <a href="https://publications.waset.org/abstracts/19254/ant-colony-optimization-control-for-multilevel-statcom" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/19254.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">556</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">591</span> Bounds on the Laplacian Vertex PI Energy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ezgi%20Kaya">Ezgi Kaya</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Dilek%20Maden"> A. Dilek Maden</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A topological index is a number related to graph which is invariant under graph isomorphism. In theoretical chemistry, molecular structure descriptors (also called topological indices) are used for modeling physicochemical, pharmacologic, toxicologic, biological and other properties of chemical compounds. Let G be a graph with n vertices and m edges. For a given edge uv, the quantity nu(e) denotes the number of vertices closer to u than v, the quantity nv(e) is defined analogously. The vertex PI index defined as the sum of the nu(e) and nv(e). Here the sum is taken over all edges of G. The energy of a graph is defined as the sum of the eigenvalues of adjacency matrix of G and the Laplacian energy of a graph is defined as the sum of the absolute value of difference of laplacian eigenvalues and average degree of G. In theoretical chemistry, the π-electron energy of a conjugated carbon molecule, computed using the Hückel theory, coincides with the energy. Hence results on graph energy assume special significance. The Laplacian matrix of a graph G weighted by the vertex PI weighting is the Laplacian vertex PI matrix and the Laplacian vertex PI eigenvalues of a connected graph G are the eigenvalues of its Laplacian vertex PI matrix. In this study, Laplacian vertex PI energy of a graph is defined of G. We also give some bounds for the Laplacian vertex PI energy of graphs in terms of vertex PI index, the sum of the squares of entries in the Laplacian vertex PI matrix and the absolute value of the determinant of the Laplacian vertex PI matrix. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=energy" title="energy">energy</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplacian%20energy" title=" Laplacian energy"> Laplacian energy</a>, <a href="https://publications.waset.org/abstracts/search?q=laplacian%20vertex%20PI%20eigenvalues" title=" laplacian vertex PI eigenvalues"> laplacian vertex PI eigenvalues</a>, <a href="https://publications.waset.org/abstracts/search?q=Laplacian%20vertex%20PI%20energy" title=" Laplacian vertex PI energy"> Laplacian vertex PI energy</a>, <a href="https://publications.waset.org/abstracts/search?q=vertex%20PI%20index" title=" vertex PI index"> vertex PI index</a> </p> <a href="https://publications.waset.org/abstracts/73194/bounds-on-the-laplacian-vertex-pi-energy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73194.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">245</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">590</span> Graph Codes - 2D Projections of Multimedia Feature Graphs for Fast and Effective Retrieval</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Stefan%20Wagenpfeil">Stefan Wagenpfeil</a>, <a href="https://publications.waset.org/abstracts/search?q=Felix%20Engel"> Felix Engel</a>, <a href="https://publications.waset.org/abstracts/search?q=Paul%20McKevitt"> Paul McKevitt</a>, <a href="https://publications.waset.org/abstracts/search?q=Matthias%20Hemmje"> Matthias Hemmje</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Multimedia Indexing and Retrieval is generally designed and implemented by employing feature graphs. These graphs typically contain a significant number of nodes and edges to reflect the level of detail in feature detection. A higher level of detail increases the effectiveness of the results but also leads to more complex graph structures. However, graph-traversal-based algorithms for similarity are quite inefficient and computation intensive, especially for large data structures. To deliver fast and effective retrieval, an efficient similarity algorithm, particularly for large graphs, is mandatory. Hence, in this paper, we define a graph-projection into a 2D space (Graph Code) as well as the corresponding algorithms for indexing and retrieval. We show that calculations in this space can be performed more efficiently than graph-traversals due to a simpler processing model and a high level of parallelization. In consequence, we prove that the effectiveness of retrieval also increases substantially, as Graph Codes facilitate more levels of detail in feature fusion. Thus, Graph Codes provide a significant increase in efficiency and effectiveness (especially for Multimedia indexing and retrieval) and can be applied to images, videos, audio, and text information. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=indexing" title="indexing">indexing</a>, <a href="https://publications.waset.org/abstracts/search?q=retrieval" title=" retrieval"> retrieval</a>, <a href="https://publications.waset.org/abstracts/search?q=multimedia" title=" multimedia"> multimedia</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20algorithm" title=" graph algorithm"> graph algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20code" title=" graph code"> graph code</a> </p> <a href="https://publications.waset.org/abstracts/135289/graph-codes-2d-projections-of-multimedia-feature-graphs-for-fast-and-effective-retrieval" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/135289.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">161</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">589</span> Construction of Graph Signal Modulations via Graph Fourier Transform and Its Applications</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Xianwei%20Zheng">Xianwei Zheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang"> Yuan Yan Tang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Classical window Fourier transform has been widely used in signal processing, image processing, machine learning and pattern recognition. The related Gabor transform is powerful enough to capture the texture information of any given dataset. Recently, in the emerging field of graph signal processing, researchers devoting themselves to develop a graph signal processing theory to handle the so-called graph signals. Among the new developing theory, windowed graph Fourier transform has been constructed to establish a time-frequency analysis framework of graph signals. The windowed graph Fourier transform is defined by using the translation and modulation operators of graph signals, following the similar calculations in classical windowed Fourier transform. Specifically, the translation and modulation operators of graph signals are defined by using the Laplacian eigenvectors as follows. For a given graph signal, its translation is defined by a similar manner as its definition in classical signal processing. Specifically, the translation operator can be defined by using the Fourier atoms; the graph signal translation is defined similarly by using the Laplacian eigenvectors. The modulation of the graph can also be established by using the Laplacian eigenvectors. The windowed graph Fourier transform based on these two operators has been applied to obtain time-frequency representations of graph signals. Fundamentally, the modulation operator is defined similarly to the classical modulation by multiplying a graph signal with the entries in each Fourier atom. However, a single Laplacian eigenvector entry cannot play a similar role as the Fourier atom. This definition ignored the relationship between the translation and modulation operators. In this paper, a new definition of the modulation operator is proposed and thus another time-frequency framework for graph signal is constructed. Specifically, the relationship between the translation and modulation operations can be established by the Fourier transform. Specifically, for any signal, the Fourier transform of its translation is the modulation of its Fourier transform. Thus, the modulation of any signal can be defined as the inverse Fourier transform of the translation of its Fourier transform. Therefore, similarly, the graph modulation of any graph signal can be defined as the inverse graph Fourier transform of the translation of its graph Fourier. The novel definition of the graph modulation operator established a relationship of the translation and modulation operations. The new modulation operation and the original translation operation are applied to construct a new framework of graph signal time-frequency analysis. Furthermore, a windowed graph Fourier frame theory is developed. Necessary and sufficient conditions for constructing windowed graph Fourier frames, tight frames and dual frames are presented in this paper. The novel graph signal time-frequency analysis framework is applied to signals defined on well-known graphs, e.g. Minnesota road graph and random graphs. Experimental results show that the novel framework captures new features of graph signals. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=graph%20signals" title="graph signals">graph signals</a>, <a href="https://publications.waset.org/abstracts/search?q=windowed%20graph%20Fourier%20transform" title=" windowed graph Fourier transform"> windowed graph Fourier transform</a>, <a href="https://publications.waset.org/abstracts/search?q=windowed%20graph%20Fourier%20frames" title=" windowed graph Fourier frames"> windowed graph Fourier frames</a>, <a href="https://publications.waset.org/abstracts/search?q=vertex%20frequency%20analysis" title=" vertex frequency analysis"> vertex frequency analysis</a> </p> <a href="https://publications.waset.org/abstracts/63133/construction-of-graph-signal-modulations-via-graph-fourier-transform-and-its-applications" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/63133.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">341</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">588</span> Enhanced Retrieval-Augmented Generation (RAG) Method with Knowledge Graph and Graph Neural Network (GNN) for Automated QA Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhihao%20Zheng">Zhihao Zheng</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhilin%20Wang"> Zhilin Wang</a>, <a href="https://publications.waset.org/abstracts/search?q=Linxin%20Liu"> Linxin Liu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the research of automated knowledge question-answering systems, accuracy and efficiency are critical challenges. This paper proposes a knowledge graph-enhanced Retrieval-Augmented Generation (RAG) method, combined with a Graph Neural Network (GNN) structure, to automatically determine the correctness of knowledge competition questions. First, a domain-specific knowledge graph was constructed from a large corpus of academic journal literature, with key entities and relationships extracted using Natural Language Processing (NLP) techniques. Then, the RAG method's retrieval module was expanded to simultaneously query both text databases and the knowledge graph, leveraging the GNN to further extract structured information from the knowledge graph. During answer generation, contextual information provided by the knowledge graph and GNN is incorporated to improve the accuracy and consistency of the answers. Experimental results demonstrate that the knowledge graph and GNN-enhanced RAG method perform excellently in determining the correctness of questions, achieving an accuracy rate of 95%. Particularly in cases involving ambiguity or requiring contextual information, the structured knowledge provided by the knowledge graph and GNN significantly enhances the RAG method's performance. This approach not only demonstrates significant advantages in improving the accuracy and efficiency of automated knowledge question-answering systems but also offers new directions and ideas for future research and practical applications. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=knowledge%20graph" title="knowledge graph">knowledge graph</a>, <a href="https://publications.waset.org/abstracts/search?q=graph%20neural%20network" title=" graph neural network"> graph neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=retrieval-augmented%20generation" title=" retrieval-augmented generation"> retrieval-augmented generation</a>, <a href="https://publications.waset.org/abstracts/search?q=NLP" title=" NLP"> NLP</a> </p> <a href="https://publications.waset.org/abstracts/188751/enhanced-retrieval-augmented-generation-rag-method-with-knowledge-graph-and-graph-neural-network-gnn-for-automated-qa-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188751.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">39</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">587</span> On Chromaticity of Wheels</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zainab%20Yasir%20Abed%20Al-Rekaby">Zainab Yasir Abed Al-Rekaby</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdul%20Jalil%20M.%20Khalaf"> Abdul Jalil M. Khalaf</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if they share the same chromatic polynomial. A Graph G is chromatically unique, if G is isomorphic to H for any graph H such that G is chromatically equivalent to H. The study of chromatically equivalent and chromatically unique problems is called chromaticity. This paper shows that a wheel W12 is chromatically unique. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=chromatic%20polynomial" title="chromatic polynomial">chromatic polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=chromatically%20equivalent" title=" chromatically equivalent"> chromatically equivalent</a>, <a href="https://publications.waset.org/abstracts/search?q=chromatically%20unique" title=" chromatically unique"> chromatically unique</a>, <a href="https://publications.waset.org/abstracts/search?q=wheel" title=" wheel"> wheel</a> </p> <a href="https://publications.waset.org/abstracts/12874/on-chromaticity-of-wheels" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12874.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">431</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=4">4</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=5">5</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=6">6</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=7">7</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=8">8</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=9">9</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=10">10</a></li> <li class="page-item disabled"><span class="page-link">...</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=20">20</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=21">21</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=multilevel%20graph&page=2" rel="next">&rsaquo;</a></li> </ul> </div> </main> <footer> <div id="infolinks" class="pt-3 pb-2"> <div class="container"> <div style="background-color:#f5f5f5;" class="p-3"> <div class="row"> <div class="col-md-2"> <ul class="list-unstyled"> About <li><a href="https://waset.org/page/support">About Us</a></li> <li><a href="https://waset.org/page/support#legal-information">Legal</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/WASET-16th-foundational-anniversary.pdf">WASET celebrates its 16th foundational anniversary</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Account <li><a href="https://waset.org/profile">My Account</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Explore <li><a href="https://waset.org/disciplines">Disciplines</a></li> <li><a href="https://waset.org/conferences">Conferences</a></li> <li><a href="https://waset.org/conference-programs">Conference Program</a></li> <li><a href="https://waset.org/committees">Committees</a></li> <li><a href="https://publications.waset.org">Publications</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Research <li><a href="https://publications.waset.org/abstracts">Abstracts</a></li> <li><a href="https://publications.waset.org">Periodicals</a></li> <li><a href="https://publications.waset.org/archive">Archive</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Open Science <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Philosophy.pdf">Open Science Philosophy</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Science-Award.pdf">Open Science Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Open-Society-Open-Science-and-Open-Innovation.pdf">Open Innovation</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Postdoctoral-Fellowship-Award.pdf">Postdoctoral Fellowship Award</a></li> <li><a target="_blank" rel="nofollow" href="https://publications.waset.org/static/files/Scholarly-Research-Review.pdf">Scholarly Research Review</a></li> </ul> </div> <div class="col-md-2"> <ul class="list-unstyled"> Support <li><a href="https://waset.org/page/support">Support</a></li> <li><a href="https://waset.org/profile/messages/create">Contact Us</a></li> <li><a href="https://waset.org/profile/messages/create">Report Abuse</a></li> </ul> </div> </div> </div> </div> </div> <div class="container text-center"> <hr style="margin-top:0;margin-bottom:.3rem;"> <a href="https://creativecommons.org/licenses/by/4.0/" target="_blank" class="text-muted small">Creative Commons Attribution 4.0 International License</a> <div id="copy" class="mt-2">© 2024 World Academy of Science, Engineering and Technology</div> </div> </footer> <a href="javascript:" id="return-to-top"><i class="fas fa-arrow-up"></i></a> <div class="modal" id="modal-template"> <div class="modal-dialog"> <div class="modal-content"> <div class="row m-0 mt-1"> <div class="col-md-12"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> </div> </div> <div class="modal-body"></div> </div> </div> </div> <script src="https://cdn.waset.org/static/plugins/jquery-3.3.1.min.js"></script> <script src="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/js/bootstrap.bundle.min.js"></script> <script src="https://cdn.waset.org/static/js/site.js?v=150220211556"></script> <script> jQuery(document).ready(function() { /*jQuery.get("https://publications.waset.org/xhr/user-menu", function (response) { jQuery('#mainNavMenu').append(response); });*/ jQuery.get({ url: "https://publications.waset.org/xhr/user-menu", cache: false }).then(function(response){ jQuery('#mainNavMenu').append(response); }); }); </script> </body> </html>