Some Inequalities for the Atom-Bond Connectivity Index of Graph

The atom-bond connectivity index (ABC) of a graph G is defined as ABC(G) = Sigma(uv is an element of E(G))root(d(u) + d(v) - 2)/(d(u)d(v)), where d(u) is the degree of vertex u. In this work, we give lower and upper bounds for the ABC index of all connected n-vertex graphs in terms of Randic index, first Zagreb, second Zagreb and modified second Zagreb indices. As an application, the ABC index for family of molecular graphs are computed.