Hyper-Zagreb indices of graphs and its applications

Abstract

The first and second Hyper-Zagreb index of a connected graph $G$ is defined by

$$HM_{1}(G)=\sum_{uv \in E(G)}[d(u)+d(v)]^{2}$$

and

$$HM_{2}(G)=\sum_{uv \in E(G)}[d(u).d(v)]^{2}.$$

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.

Received: 30 June 2020 | Accepted: 9 September 2020