Atom-bond connectivity index of graphs Original Research Article

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