Document Zbl 1514.68220

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Comput. Sci.</a> <a href="/?q=in%3A470535" title="Articles in this Issue">889, 25-40 (2021)</a>. </div> <div class="abstract">Summary: The connectivity of a connected graph $G$ is the minimum cardinality over all vertex-cuts, which can be determined using Menger’s theorem (1927). Then $G$ is super connected if its minimum vertex-cut is always composed of a vertex’s neighborhood. Two generalized extensions to this classic notion of connectivity include the $T$-structure connectivity $\kappa(G;T)$ and the $T$-substructure connectivity $\kappa^s(G;T)$, for which $T$ is the given structure isomorphic to a connected subgraph of $G$. Let $T^\ast$ denote the union of the set of all connected subgraphs of $T$ and the set of the trivial graph. In this article, a connected graph $G$ is called super $T$-connected if the minimum degree of $G-F$ is zero for each minimum $T$-cut $F$ of $G$; analogously, $G$ is super $T^\ast$-connected if the minimum degree of $G-F$ is zero for each minimum $T^\ast$-cut $F$ of $G$. Considering the $n$-dimensional locally twisted cube $LTQ_n$ with $n\geq 3$, we first establish both $\kappa(LTQ_n; T)$ and $\kappa^s(LTQ_n;T)$ and then determine whether $LTQ_n$ is super $T$-connected and super $T^\ast$-connected, where $T\in\{K_{1,1},K_{1,2},K_{1,3}, C_4\}\cup\{P_k \mid 4\leq k\leq n\}$.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A7407469">Cited in <strong>5</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68R10" title="MSC2020">68R10</a> </td> <td class="space"> Graph theory (including graph drawing) in computer science </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C40" title="MSC2020">05C40</a> </td> <td class="space"> Connectivity </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68M15" title="MSC2020">68M15</a> </td> <td class="space"> Reliability, testing and fault tolerance of networks and computer systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aconnectivity">connectivity</a>; <a href="/?q=ut%3Astructure+connectivity">structure connectivity</a>; <a href="/?q=ut%3Asuper-connectedness">super-connectedness</a>; <a href="/?q=ut%3Alocally+twisted+cubes">locally twisted cubes</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 1514.68220" data-ciurl="/ci/07407469" data-biburl="/bibtex/07407469.bib" data-amsurl="/amsrefs/07407469.bib" data-xmlurl="/xml/07407469.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/07407469.pdf" title="Zbl 1514.68220 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/10.1016/j.tcs.2021.07.034" aria-label="DOI for “Super fault-tolerance assessment of locally twisted cubes based on the structure connectivity”" title="10.1016/j.tcs.2021.07.034">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">Abraham, S.; Padmanabhan, K., The twisted cube topology for multiprocessors: a study in networks asymmetry, J. 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