Hyper-Zagreb indices of graphs and its applications

Year 2021, Volume: 8 Issue: 1, 9 - 22, 15.01.2021

Girish V. Rajasekharaiah Usha P. Murthy

https://doi.org/10.13069/jacodesmath.867532

Cited By: 13

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.

Keywords

Degree of a vertex, Hyper-Zagreb index, Molecular graph

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