Commun. Korean Math. Soc. 2021; 36(2): 389-400
Online first article March 4, 2021 Printed April 30, 2021
https://doi.org/10.4134/CKMS.c190227
Copyright © The Korean Mathematical Society.
Jianwei Du, Xiaoling Sun
North University of China; North University of China
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)
2020; 35(1): 1-12
2015; 30(3): 283-295
1997; 12(1): 27-36
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