Exact Values of Zagreb Indices for Generalized T-Sum Networks with Lexicographic Product

The use of numerical numbers to represent molecular networks plays a crucial role in the study of physicochemical and structural properties of the chemical compounds. For some integer k and a network G, the networks SkG and RkG are its derived networks called as generalized subdivided and generalized semitotal point networks, where Sk and Rk are generalized subdivision and generalized semitotal point operations, respectively. Moreover, for two connected networks, G1 and G2, G1G2Sk and G1G2Rk are T-sum networks which are obtained by the lexicographic product of TG1 and G2, respectively, where TεSk,Rk. In this paper, for the integral value k≥1, we find exact values of the first and second Zagreb indices for generalized T-sum networks. Furthermore, the obtained findings are general extensions of some known results for only k=1. At the end, a comparison among the different generalized T-sum networks with respect to first and second Zagreb indices is also included.