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Extremal atom-bond connectivity index of cactus graphs

Ali Reza Ashrafi|Tayebeh Dehghan-Zadeh|Nader Habibi
대한수학회 (The Korean Mathematical Society)|2015.07|대한수학회논문집 (Communications of the KMS)|제30권 제3호|pp. 283-295

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참고문헌

키워드

cactus graph$ABC$ index
주제분류수학

초록

The atom-bond connectivity index of a graph $G$ ($ABC$ index for short) is defined as the summation of quantities $\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$ over all edges of $G$. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the $ABC$ index among all $n$ vertex cactus graphs.

Abstract

The atom-bond connectivity index of a graph $G$ ($ABC$ index for short) is defined as the summation of quantities $\sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}}$ over all edges of $G$. A cactus graph is a connected graph in which every block is an edge or a cycle. The aim of this paper is to obtain the first and second maximum values of the $ABC$ index among all $n$ vertex cactus graphs.

참고문헌 (20)

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