Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

Abstract

A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs $G_1$ and $G_2$ , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs $T_k\left(G_1\right)$ and $G_2$ , where $T_k\left(G_1\right)$ is obtained by applying the generalized total operation $T_k$ on $G_1$ with $k\ge 1$ as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product.