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 S-k(G) and R-k(G) are its derived networks called as generalized subdivided and generalized semitotal point networks, where S-k and R-k are generalized subdivision and generalized semitotal point operations, respectively. Moreover, for two connected networks, G(1) and G(2), G(1)[G(2)](Sk) and G(1)[G(2)](Rk) are T-sum networks which are obtained by the lexicographic product of T(G(1)) and G(2), respectively, where T epsilon{S-k, R-k} 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.