On chromatic and flow polynomial unique graphs

Yinghua Duan, Haidong Wu, Qinglin Yu
<span title="">2008</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/lx7dev2le5anbg6oarljwh7lie" style="color: black;">Discrete Applied Mathematics</a> </i> &nbsp;
It is known that the chromatic polynomial and flow polynomial of a graph are two important evaluations of its Tutte polynomial, both of which contain much information of the graph. Much research is done on graphs determined entirely by their chromatic polynomials and Tutte polynomials, respectively. Oxley asked which classes of graphs or matroids are determined by their chromatic and flow polynomials together. In this paper, we found several classes of graphs with this property. We first study
more &raquo; ... hich graphic parameters are determined by the flow polynomials. Then we study flow-unique graphs. Finally, we show that several classes of graphs, ladders, Möbius ladders and squares of n-cycle are determined by their chromatic polynomials and flow polynomials together. A direct consequence of our theorem is a result of de Mier and Noy [A. de Mier, M. Noy, On graphs determined by their Tutte polynomial, Graphs Comb. 20 (2004) 105-119] that these classes of graphs are Tutte polynomial unique.
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2007.10.010">doi:10.1016/j.dam.2007.10.010</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6fxjxx7owfh73orj6su54oih7m">fatcat:6fxjxx7owfh73orj6su54oih7m</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20190415234308/https://core.ac.uk/download/pdf/82135128.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e1/74/e1743ea01d9645f1bf2b19d3afdc946e7bc5ca6c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.dam.2007.10.010"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>