Multiplicative Zagreb Indices of Molecular Graphs

Abstract

Mathematical modeling with the help of numerical coding of graphs has been used in the different fields of science, especially in chemistry for the studies of the molecular structures. It also plays a vital role in the study of the quantitative structure activities relationship (QSAR) and quantitative structure properties relationship (QSPR) models. Todeshine et al. (2010) and Eliasi et al. (2012) defined two different versions of the 1st multiplicative Zagreb index as ∏Γ=∏p⋯VΓdΓp2 and ∏1Γ=∏pq⋯EΓdΓp+dΓq, respectively. In the same paper of Todeshine, they also defined the 2nd multiplicative Zagreb index as ∏2Γ=∏pq⋯EΓdΓp×dΓq. Recently, Liu et al. [IEEE Access; 7(2019); 105479 - 105488] defined the generalized subdivision-related operations of graphs and obtained the generalized F-sum graphs using these operations. They also computed the first and second Zagreb indices of the newly defined generalized F-sum graphs. In this paper, we extend this study and compute the upper bonds of the first multiplicative Zagreb and second multiplicative Zagreb indices of the generalized F-sum graphs. At the end, some particular results as applications of the obtained results for alkane are also included.