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Variable sum exdeg indices of cactus graphs

Jianwei Du|Xiaoling Sun
대한수학회 (The Korean Mathematical Society)|2021.04|대한수학회논문집 (Communications of the KMS)|제36권 제2호|pp. 389-400|DOI 10.4134/CKMS.c190227

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참고문헌

키워드

cycleVariable sum exdeg indexcactus graphpendant vertex
주제분류수학

초록

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.

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.

참고문헌 (26)

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