Hyper-Zagreb indices of graphs and its applications
Girish V. Rajasekharaiah, Usha P. MURTHY
2021Journal of Algebra Combinatorics Discrete Structures and Applications31 citationsDOIOpen Access PDF
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.
Topics & Concepts
CombinatoricsMathematicsGraphIndex (typography)Linear regressionStatisticsComputer scienceWorld Wide WebGraph theory and applicationsComputational Drug Discovery MethodsSynthesis and Properties of Aromatic Compounds