Hyper-Zagreb index of graphs based on generalized subdivision related operationsHyper-Zagreb index of graphs based on generalized subdivision related operations

Abstract

Mathematical modeling of the molecular graphs plays a fundamental part in the analysis of the quantitative structures activity relationship (QSAR) and quantitative structures property relationship models (QSPR models). In 2013, Shirdel et. al. [IJMC; 4(2013); 213-220] defined the new topological index of a graph (Γ) named as hyper-Zagreb index [HM(Γ)] is HM(Γ) = P yz²E(Γ) [dΓ(y) + dΓ(z)]2 Liu et al. [IEEE Access; 7(2019); 105479-105488] defined the concept of the generalized subdivision operations on graphs and obtained the generalized F-sum graphs. In this paper, the hyper-Zagreb index is calculated for the generalized F-sum graphs in terms of their factor graphs. In fact, the obtained results are the general extension of the results Anandkumar et al. [IJPAM; 112(2017); 239-252]