Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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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.

Variable sum exdeg indices of cactus graphs

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)