Augmented Zagreb Index of Connected Graphs

The augmented Zagreb index of a graph G is defined to be AZI(G) = Sigma(uv is an element of E(G)) (d(u) d(v)/d(u) + d(v) - 2)(3), where E(G) is the edge set of G, d(u) and d(v) are the degrees of the terminal vertices and v of edge ay. Such recently introduced topological index has proven to be a valuable predictive index in the study of the heat of formation of octanes and heptanes. In this paper, we present upper and lower bounds on the augmented Zagreb index for various classes of connected graphs, and characterize the corresponding extremal graphs.