Document Zbl 1398.05167

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Math.</a> <a href="/?q=in%3A418314" title="Articles in this Issue">250, 342-356 (2018)</a>. </div> <div class="abstract">Summary: The anti-forcing number of a perfect matching $M$ of a graph $G$ is the minimal number of edges of $G$ not in $M$ whose deletion results in a subgraph with a unique perfect matching $M$. The maximum anti-forcing number of a benzenoid system $H$ equals the Fries number of $H$. <span class="zbmathjax-textit">H.-K. Hwang</span> et al. [“Distribution of forcing and anti-forcing numbers of random perfect matchings on hexagonal chains and crowns”, Preprint, <a href="http://140.109.74.92/hk/wp-content/files//2015/01/distribution_of_the_forcing_and_anti-forcing_numbers.pdf">http://140.109.74.92/hk/wp-content/files//2015/01/distribution_of_the_forcing_and_anti-forcing_numbers.pdf</a>] defined the anti-forcing polynomial of a graph as a counting polynomial for perfect matchings with the same anti-forcing number, and obtained explicit expressions of the anti-forcing polynomial of hexagonal chains and crowns. In this paper, we focus on benzenoid systems with forcing edges, and obtain a recurrence relation of their anti-forcing polynomial. Furthermore, we get an explicit expression of the anti-forcing polynomial of benzenoid parallelograms.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6966423">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%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%3A05C31" title="MSC2020">05C31</a> </td> <td class="space"> Graph polynomials </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Aperfect+matching">perfect matching</a>; <a href="/?q=ut%3Aanti-forcing+number">anti-forcing number</a>; <a href="/?q=ut%3Aanti-forcing+polynomial">anti-forcing polynomial</a>; <a href="/?q=ut%3Abenzenoid+system">benzenoid system</a>; <a href="/?q=ut%3Aforcing+edge">forcing edge</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 1398.05167" data-ciurl="/ci/06966423" data-biburl="/bibtex/06966423.bib" data-amsurl="/amsrefs/06966423.bib" data-xmlurl="/xml/06966423.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06966423.pdf" title="Zbl 1398.05167 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.2018.05.023" aria-label="DOI for “Anti-forcing polynomials for benzenoid systems with forcing edges”" title="10.1016/j.dam.2018.05.023">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">Barahona, F.; Fonlupt, J.; Mahjoub, A. 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