# EXTREMAL ATOM-BOND CONNECTIVITY INDEX OF CACTUS GRAPHS

• ASHRAFI, ALI REZA (Department of Pure Mathematics Faculty of Mathematical Science University of Kashan) ;
• DEHGHAN-ZADEH, TAYEBEH (Department of Pure Mathematics Faculty of Mathematical Science University of Kashan) ;
• HABIBI, NADER (Department of Mathematics Faculty of Science University of Ayatollah Ozma Boroujerdi)
• Published : 2015.06.30
• 77 23

#### 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

#### Acknowledgement

Supported by : University of Kashan

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