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 G1 and G2, we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs TkG1 and G2, where TkG1 is obtained by applying the generalized total operation Tk on G1 with k≥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.