Graph Indices for Cartesian Product of -sum of Connected Graphs

Abstract

Background: A topological index is a real number associated with a graph that provides information about its physical and chemical properties and their correlations. Topological indices are being used successfully in Chemistry, Computer Science, and many other fields.

Methods: In this article, we apply the well-known Cartesian product on F-sums of connected and finite graphs. We formulate sharp limits for some famous degree-dependent indices.

Results: Zagreb indices for the graph operations T(G), Q(G), S(G), R(G), and their F-sums have been computed. By using orders and sizes of component graphs, we derive bounds for Zagreb indices, F-index, and Narumi-Katayana index.

Conclusion: The formulation of expressions for the complicated products on F-sums, in terms of simple parameters like maximum and minimum degrees of basic graphs, reduces the computational complexities.

Keywords: Augmented Zagreb index; Cartesian product; F-index.; F-sum of graphs; Narumi-Katayana index; Zagreb index.