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arXiv · 1505.05496

Further results regarding the degree resistance distance of cacti

Jia-Bao Liu·Wen-Rui Wang·Yong-Ming Zhang·Xiang-Feng Pan
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Abstract

A graph $G$ is called a cactus if each block of $G$ is either an edge or a cycle. Denote by $Cact(n;t)$ the set of connected cacti possessing $n$ vertices and $t$ cycles. In this paper, we show that there are some errors in [J. Du, G. Su, J. Tu, I. Gutman, The degree resistance distance of cacti, Discrete Appl. Math. 188 (2015) 16-24.], and we present some results which correct their mistakes. We also give the second-minimum and third-minimum degree resistance distances among graphs in $Cact(n;t)$, and characterize the corresponding extremal graphs as well.

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Jia-Bao Liu, Wen-Rui Wang, Yong-Ming Zhang, Xiang-Feng Pan. 2015-05-18. Further results regarding the degree resistance distance of cacti. https://arxiv.org/abs/1505.05496

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