Document Zbl 1520.05027

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Naresh</a>; <a href="/authors/venkatakrishnan.yanamandram-balasubramanian" title="Author Profile">Venkatakrishnan, Y. B.</a>; <a href="/authors/raja.s-p" title="Author Profile">Raja, S. P.</a></div> <h2 class="title"> <strong>On the computation of extremal trees of harmonic index with given edge-vertex domination number.</strong> <i>(English)</i> <a class="label nowrap" href="/1520.05027">Zbl 1520.05027</a> </h2> <div class="source"> <a href="/serials/3137" title="Journal Profile">Int. J. Wavelets Multiresolut. Inf. Process.</a> <a href="/?q=in%3A502283" title="Articles in this Issue">21, No. 5, Article ID 2350014, 12 p. (2023)</a>. </div> <div class="abstract">Summary: Let $v_1, v_2$ be vertices of a graph $G$ with degree of the vertices being $d(v_1)$ and $d(v_2)$, respectively. First, let us define the weight of the edge $v_1v_2$ as twice the value of $\frac{1}{d(v_1)+d(v_2)}$ in $G$. Let us define $H(G)$, the harmonic index of the graph $G$, as the sum obtained by adding the weight assigned to every edge of $G$. In this paper, for the class of trees, we shall obtain an upper bound for the harmonic index $H(G)$ in terms of the edge-vertex domination number and the order of $G$. Also, we shall ascertain that the equality is true by characterizing the collection of all extremal trees attaining this bound.</div> <div class="clear"></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C09" title="MSC2020">05C09</a> </td> <td class="space"> Graphical indices (Wiener index, Zagreb index, Randić index, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C07" title="MSC2020">05C07</a> </td> <td class="space"> Vertex degrees </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C35" title="MSC2020">05C35</a> </td> <td class="space"> Extremal problems in graph theory </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C92" title="MSC2020">05C92</a> </td> <td class="space"> Chemical graph theory </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Atrees">trees</a>; <a href="/?q=ut%3Aedge-vertex+domination+number">edge-vertex domination number</a>; <a href="/?q=ut%3Aharmonic+index">harmonic index</a></div> <div class="software"> <h3>Software:</h3><a href="/software/7495">GRAFFITI</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1520.05027" data-ciurl="/ci/07741304" data-biburl="/bibtex/07741304.bib" data-amsurl="/amsrefs/07741304.bib" data-xmlurl="/xml/07741304.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07741304.pdf" title="Zbl 1520.05027 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1142/S0219691323500145" aria-label="DOI for “On the computation of extremal trees of harmonic index with given edge-vertex domination number”" title="10.1142/S0219691323500145">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">Andriulli, F. 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Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching. </div> </div></article> </div></div> </div> </div> <div class="clearfix"></div> </div> </div> <div id="foot"><div class="copyright"> © 2025 <a target="fiz" href="https://www.fiz-karlsruhe.de/en">FIZ Karlsruhe GmbH</a> <a href="/privacy-policy/">Privacy Policy</a> <a href="/legal-notices/">Legal Notices</a> <a href="/terms-conditions/">Terms & Conditions</a> <div class="info"> <ul class="nav"> <li class="mastodon"> <a href="https://mathstodon.xyz/@zbMATH" target="_blank" class="no-new-tab-icon"> <img src="/static/mastodon.png" title="zbMATH at Mathstodon (opens in new tab)" alt="Mastodon logo"> </a> </li> </ul> </div> </div> <div class="clearfix" style="height: 0px;"></div> </div> </div> <script src="https://static.zbmath.org/contrib/jquery/1.9.1/jquery.min.js"></script> <script src="https://static.zbmath.org/contrib/jquery-caret/1.5.2/jquery.caret.min.js"></script> <script src="/static/js/jquery-ui-1.10.1.custom.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap/v3.3.7zb1/js/bootstrap.min.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-lightbox/v0.7.0/bootstrap-lightbox.min.js"></script> <script src="https://static.zbmath.org/contrib/retina/unknown/retina.js"></script> <script src="https://static.zbmath.org/contrib/bootstrap-select/v1.13.14/js/bootstrap-select.min.js"></script> <script> var SCRIPT_ROOT = ""; </script> <script src="/static/scripts.js?v=20240926"> </script> <script src="https://static.zbmath.org/contrib/mathjax/2.7.1/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script> <script type="text/x-mathjax-config"> MathJax.Hub.Config({ "HTML-CSS": { preferredFont: "TeX", availableFonts: [ "STIX", "TeX" ], linebreaks: { automatic: true }, EqnChunk: (MathJax.Hub.Browser.isMobile ? 10 : 50) }, tex2jax: { processEscapes: true, ignoreClass: "tex2jax_ignore|dno" }, TeX: { Macros: { Aut: "\\operatorname{Aut}", Hom: "\\operatorname{Hom}" }, noUndefined: { attributes: { mathcolor: "#039", //"red", mathbackground: "white", //"#FFEEEE", mathsize: "90%" } } }, messageStyle: "none" }); </script> <script type="text/javascript"> $(document).ready(function() { $("#MathInput").stop(true, true).keyup(function() { $.ajax({ url: "/mwsq/", type: "POST", data: { query : $("#MathInput").val() }, dataType: "text" }) .done(function(xml) { $("#MathPreview").html(xml); $(window).resize(); }); }); var press = jQuery.Event("keyup"); press.ctrlKey = false; press.which = 40; $("#MathInput").trigger(press); }); </script> <div id="new_tab_icon" style="display: none"> <span class="glyphicon glyphicon-new-window" aria-hidden="true"></span><span class="sr-only">(opens in new tab)</span></div> </body> </html>

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