Iranian Journal of Mathematical Chemistry
https://ijmc.kashanu.ac.ir/
Iranian Journal of Mathematical Chemistryendaily1Sun, 01 May 2022 00:00:00 +0430Sun, 01 May 2022 00:00:00 +0430The Schultz Index for Product Graphs
https://ijmc.kashanu.ac.ir/article_111996.html
Among the binary operations made with graphs&lrm;, &lrm;the cartesian&lrm;, &lrm;corona&lrm;, &lrm;and lexicographic are three well-known products&lrm;, &lrm;as well as the cartesian sum&lrm;. &lrm;Topological indices are graph invariants used to describe graphs associated with molecules&lrm;, &lrm;one of these is the Schultz index&lrm;, &lrm;which can be obtained as&lrm; &lrm; &lrm;&sum; u&ne;v (deg u+ deg v) d(u,v), &lrm;where the sum runs over all pairs of distinct vertices of the graph&lrm;. &lrm;In this paper&lrm;, &lrm;we give explicit expressions for the Schultz index of cartesian and corona&lrm;, &lrm;with alternative proofs to those given in the literature&lrm;, &lrm;as well as for lexicographic product and the cartesian sum&lrm;, &lrm;all of these formulas involve order and size of factors&lrm;, &lrm;additionally&lrm;, &lrm;the first three involve both Wiener and Schultz indices of factors&lrm;, &lrm;corona and lexicographic also involve Zagreb index and the last one just Zagreb.&lrm; &lrm;