Resistance distances and Kirchhoff index of graphs with an involution

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• 作者：Liyuan Shi ^{liyuans5@163.com" class="auth_mail" title="E-mail the corresponding author} ; Haiyan Chen ; ^{chey5@jmu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Resistance distance ; Kirchhoff index ; Involution ; Laplacian matrix
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：31 December 2016
• 年：2016
• 卷：215
• 期：Complete
• 页码：185-196
• 全文大小：464 K

文摘

Motivated by the work of Zhang and Yan (2009), this paper considers the problem of computing resistance distances and Kirchhoff index of graphs with an involution. We show that if class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303109&_mathId=si1.gif&_user=111111111&_pii=S0166218X16303109&_rdoc=1&_issn=0166218X&md5=94ceb84067e99a543ce18465cb2c916c" title="Click to view the MathML source">Gclass="mathContainer hidden">class="mathCode">$G$ is a weighted graph with an involution, then the resistance distance and the Kirchhoff index of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303109&_mathId=si1.gif&_user=111111111&_pii=S0166218X16303109&_rdoc=1&_issn=0166218X&md5=94ceb84067e99a543ce18465cb2c916c" title="Click to view the MathML source">Gclass="mathContainer hidden">class="mathCode">$G$ can be expressed in terms of parameters of two weighted graphs with a smaller size. As applications, we compute resistance distances and Kirchhoff indices of double graphs, the almost-complete graph and the almost-complete bipartite graph.