Document Zbl 1365.05121

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Although the complete classification is left open, we derive infinite and non-trivial classes of both Cayley and non-Cayley graphs. We give a complete classification of the case when $k=2$, showing that $S_{n,2}$ is Cayley if and only if $n$ is a prime power. We also give a sufficient condition for $S_{n,3}$ to be Cayley and study other structural properties, such as demonstrating that $S_{n,k}$ always has a uniform shortest path routing.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=ci%3A6737152">Cited in <strong>1</strong> Review</a></div><div class="clear"><a href="/?q=rf%3A6737152">Cited in <strong>3</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C25" title="MSC2020">05C25</a> </td> <td class="space"> Graphs and abstract algebra (groups, rings, fields, etc.) </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A05C82" title="MSC2020">05C82</a> </td> <td class="space"> Small world graphs, complex networks (graph-theoretic aspects) </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Ainterconnection+networks">interconnection networks</a>; <a href="/?q=ut%3ACayley+graphs">Cayley graphs</a>; <a href="/?q=ut%3Avertex-forwarding+index">vertex-forwarding index</a>; <a href="/?q=ut%3A%5C%28%28n%2C+k%29%5C%29-star+graphs">$(n, k)$-star graphs</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 1365.05121" data-ciurl="/ci/06737152" data-biburl="/bibtex/06737152.bib" data-amsurl="/amsrefs/06737152.bib" data-xmlurl="/xml/06737152.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06737152.pdf" title="Zbl 1365.05121 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/10.1007/s00373-016-1741-8" aria-label="DOI for “On the problem of determining which $(n, k)$-star graphs are Cayley graphs”" title="10.1007/s00373-016-1741-8">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">Araki, T.: Hyper Hamiltonian laceability of Cayley graphs generated by transpositions. 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