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(G(1)) and G(2), where T-k(G(1)) 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.