Atom-bond connectivity index of graphs

The recently introduced atom-bond connectivity (ABCABC) index has been applied up until now to study the stability of alkanes and the strain energy of cycloalkanes. Furtula et al. (2009) [3] obtained extremal ABCABC values for chemical trees, and also, it has been shown that the star K1,n−1K1,n−1, has the maximal ABCABC value of trees. In this paper, we present the lower and upper bounds on ABCABC index of graphs and trees, and characterize graphs for which these bounds are best possible.