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http://dx.doi.org/10.4134/CKMS.2015.30.3.283

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)
Publication Information
Communications of the Korean Mathematical Society / v.30, no.3, 2015 , pp. 283-295 More about this Journal
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;
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