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 S k and G 1 G 2 R k are T -sum networks which are obtained by the lexicographic product of T G 1 and G 2 , respectively, where T ε 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.