On degree resistance distance of cacti

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• 作者：Jia-Bao Liu^a ; ^b ; ^{liujiabaoad@163.com" class="auth_mail" title="E-mail the corresponding author} ; Wen-Rui Wang^a ; ^{Ricciawang@163.com" class="auth_mail" title="E-mail the corresponding author} ; Yong-Ming Zhang^a ; ^{ymzhang625@163.com" class="auth_mail" title="E-mail the corresponding author} ; Xiang-Feng Pan^a ; ^{xfpan@ahu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; ^{xfpan@ustc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Cactus ; Resistance distance ; Degree resistance distance ; Kirchhoff index
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：20 April 2016
• 年：2016
• 卷：203
• 期：Complete
• 页码：217-225
• 全文大小：461 K

文摘

A graph class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004667&_mathId=si19.gif&_user=111111111&_pii=S0166218X15004667&_rdoc=1&_issn=0166218X&md5=e3fdf231cfd5ac15406f619809d8ccf6" title="Click to view the MathML source">Gclass="mathContainer hidden">class="mathCode">$G$ is called a cactus if each block of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004667&_mathId=si19.gif&_user=111111111&_pii=S0166218X15004667&_rdoc=1&_issn=0166218X&md5=e3fdf231cfd5ac15406f619809d8ccf6" title="Click to view the MathML source">Gclass="mathContainer hidden">class="mathCode">$G$ is either an edge or a cycle. Denote by class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004667&_mathId=si21.gif&_user=111111111&_pii=S0166218X15004667&_rdoc=1&_issn=0166218X&md5=597e10ab91e333dc74a6eba2bd494076" title="Click to view the MathML source">Cact(n;t)class="mathContainer hidden">class="mathCode">$Cact(n;t)$ the set of connected cacti possessing class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004667&_mathId=si22.gif&_user=111111111&_pii=S0166218X15004667&_rdoc=1&_issn=0166218X&md5=fa8e5158024c49ea3a1b91f67782096d" title="Click to view the MathML source">nclass="mathContainer hidden">class="mathCode">$n$ vertices and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004667&_mathId=si23.gif&_user=111111111&_pii=S0166218X15004667&_rdoc=1&_issn=0166218X&md5=99d9be3bdde896b7eac27b64f54aeb0f" title="Click to view the MathML source">tclass="mathContainer hidden">class="mathCode">$t$ cycles. In a recent paper (Du et al., 2015), the class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004667&_mathId=si21.gif&_user=111111111&_pii=S0166218X15004667&_rdoc=1&_issn=0166218X&md5=597e10ab91e333dc74a6eba2bd494076" title="Click to view the MathML source">Cact(n;t)class="mathContainer hidden">class="mathCode">$Cact(n;t)$ with minimum degree resistance distance was characterized. We now determine the elements of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X15004667&_mathId=si21.gif&_user=111111111&_pii=S0166218X15004667&_rdoc=1&_issn=0166218X&md5=597e10ab91e333dc74a6eba2bd494076" title="Click to view the MathML source">Cact(n;t)class="mathContainer hidden">class="mathCode">$Cact(n;t)$ with second-minimum and third-minimum degree resistance distances. In addition, some mistakes in Du et al. (2015) are pointed out.