仙人掌图的一般Atom-Bond Sum-connectivity指数

The general Atom-Bond Sum-connectivity index of cactus graphs

摘要

图G的一般Atom-Bond Sum-connectivity指数被定义为
$A B S_{\alpha}(G)=\sum_{u v \in E(G)}\left(\frac{d(u)+d(v)-2}{d(u)+d(v)}\right)^{\alpha},$
其中d(u)和d(v)分别表示G中顶点u和v的度,α是一个任意的实数。如果图G中任意两个圈之间最多只有一个公共顶点,则称图G为仙人掌图。本文给出了n阶仙人掌图的ABS_α(G)指数的极值,并且刻画了相应的极图。

Abstract

The general Atom-Bond Sum-connectivity index of a graph G is defined as
$A B S_{\alpha}(G)=\sum_{u v \in E(G)}\left(\frac{d(u)+d(v)-2}{d(u)+d(v)}\right)^{\alpha},$
where d(u) and d(v) denote the degree of the vertex u and v in G respectively, and α is an arbitrary real number. A graph G is called a cactus graph if there is at most one common vertex between any two cycles in the graph. This paper provides the extremal values of the ABS_α(G) index of cactus graphs with order n, and characterizes the corresponding extremal graphs.

关键词

仙人掌图 / Atom-Bond Sum-connectivity指数 / 极值图

Key words

cactus graph / Atom-Bond Sum-connectivity index / extremal graph

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基金资助

宁夏回族自治区自然科学基金项目(2024AAC03011)