Document Zbl 1246.05126

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Math.</a> <a href="/?q=in%3A302816" title="Articles in this Issue">160, No. 13-14, 1936-1954 (2012)</a>. </div> <div class="abstract">Summary: The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor almost-perfect matchings. For many interconnection networks, the optimal sets are precisely those induced by a single vertex.<br class="zbmathjax-paragraph"> Recently, the conditional matching preclusion number of a graph was introduced to look for obstruction sets beyond those induced by a single vertex. It is defined to be the minimum number of edges whose deletion results in a graph with no isolated vertices and neither perfect matchings nor almost-perfect matchings.<br class="zbmathjax-paragraph"> In this paper, we prove general results regarding the matching preclusion number and the conditional matching preclusion number as well as the classification of their respective optimal sets for regular graphs. We then use these general results to study the problems for Cayley graphs generated by 2-trees and the hyper Petersen networks.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6064582">Cited in <strong>32</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C70" title="MSC2020">05C70</a> </td> <td class="space"> Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A68M10" title="MSC2020">68M10</a> </td> <td class="space"> Network design and communication in computer systems </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainterconnection+networks">interconnection networks</a>; <a href="/?q=ut%3Aperfect+matching">perfect matching</a>; <a href="/?q=ut%3Aregular+graphs">regular graphs</a>; <a href="/?q=ut%3Amatching+preclusion">matching preclusion</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 1246.05126" data-ciurl="/ci/06064582" data-biburl="/bibtex/06064582.bib" data-amsurl="/amsrefs/06064582.bib" data-xmlurl="/xml/06064582.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06064582.pdf" title="Zbl 1246.05126 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.dam.2012.03.040" aria-label="DOI for “Matching preclusion and conditional matching preclusion for regular interconnection networks”" title="10.1016/j.dam.2012.03.040">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">Al-Ayyoub, A.-E.; Day, K., Comparative study of product networks, Journal of Parallel and Distributed Computing, 62, 1-18 (2002) · <a href="/1006.68001" class="nowrap">Zbl 1006.68001</a></td> </tr><tr> <td>[2]</td> <td class="space">Beineke, L. 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