The Atom Bond Connectivity Index of Some Trees and Bicyclic Graphs

Abstract

The atom bond connectivity (ABC) index is one of the recently most investigated degree-based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as \( ABC(G) = \sum\nolimits_{uv \in E(G)} {\sqrt {d_{v} + d_{u} - 2/d_{v} \cdot d_{u} } } \), where d u denotes the degree of a vertex u in G. In this paper, we obtain the general formula for ABC index of some special, chemical trees, and bicyclic graphs.