Extremal atom-bond connectivity index of cactus graphs

Ali Reza Ashrafi; Tayebeh Dehghan-Zadeh; Nader Habibi

doi:10.4134/CKMS.2015.30.3.283

Communications of the
Korean Mathematical Society CKMS

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

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Commun. Korean Math. Soc. 2015; 30(3): 283-295

Printed July 31, 2015

https://doi.org/10.4134/CKMS.2015.30.3.283

Extremal atom-bond connectivity index of cactus graphs

Ali Reza Ashrafi, Tayebeh Dehghan-Zadeh, and Nader Habibi

University of Kashan, University of Kashan, University of Ayatollah Ozma Boroujerdi

Abstract

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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.

Keywords: $ABC$ index, cactus graph

MSC numbers: 05C07, 05C35