Hyper-Zagreb indices of graphs and its applications

Abstract

The first and second Hyper-Zagreb index of a connected graph G is defined by HM1(G) = ∑ uv∈E(G)[d(u) +d(v)]2 and HM2(G) =∑uv∈E(G)[d(u).d(v)]2 . In this paper, the first and second Hyper-Zagreb indices of certain graphs are computed. Also the bounds for the first and second Hyper-Zagreb indices are determined. Further linear regression analysis of the degree based indices with the boiling points of benzenoid hydrocarbons is carried out. The linear model, based on the Hyper-Zagreb index, is better than the models corresponding to the other distance based indices.