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arxiv: 1505.05496 · v1 · pith:P6IRRC7Qnew · submitted 2015-05-18 · 🧮 math.CO · math.SP

Further results regarding the degree resistance distance of cacti

classification 🧮 math.CO math.SP
keywords cactidegreeresistancecactdistancegraphsresultssome
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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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