The Schultz Index for Product Graphs

Among the binary operations made with graphs, the cartesian, corona, and lexicographic are three well-known products, as well as the cartesian sum. Topological indices are graph invariants used to describe graphs associated with molecules, one of these is the Schultz index, which can be obtained as Sigma u not equal v (degu + degv)d(u, AT), where the sum runs over all pairs of distinct vertices of the graph. In this paper, we give explicit expressions for the Schultz index of cartesian and corona, with alternative proofs to those given in the literature, as well as for lexicographic product and the cartesian sum, all of these formulas involve order and size of factors, additionally, the first three involve both Wiener and Schultz indices of factors, corona and lexicographic also involve Zagreb index and the last one just Zagreb. (C) 2022 University of Kashan Press. All rights reserved