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 G$G$ is called a cactus if each block of G$G$ is either an edge or a cycle. Denote by Cact(n;t)$Cact(n;t)$ the set of connected cacti possessing n$n$ vertices and t$t$ cycles. In a recent paper (Du et al., 2015), the Cact(n;t)$Cact(n;t)$ with minimum degree resistance distance was characterized. We now determine the elements of Cact(n;t)$Cact(n;t)$ with second-minimum and third-minimum degree resistance distances. In addition, some mistakes in Du et al. (2015) are pointed out.