Variable sum exdeg indices of cactus graphs
Commun. Korean Math. Soc. 2021 Vol. 36, No. 2, 389-400
Published online March 4, 2021
Printed April 30, 2021
Jianwei Du, Xiaoling Sun
North University of China; North University of China
Abstract : For a graph $G$, the variable sum exdeg index $SEI_{a}(G)$ is defined as $\sum _{u\in V(G)}d_{G}(u)a^{d_{G}(u)}$, where $a\in (0,1)\cup(1,+\infty)$. In this work, we determine the minimum and maximum variable sum exdeg indices (for $a>1$) of $n$-vertex cactus graphs with $k$ cycles or $p$ pendant vertices. Furthermore, the corresponding extremal cactus graphs are characterized.
Keywords : Variable sum exdeg index, cactus graph, cycle, pendant vertex
MSC numbers : Primary 05C07, 92E10
Supported by : Xiaoling Sun is supported by the Shanxi Province Science Foundation for Youths (No. 201901D211227)
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