Graph Indices for Cartesian Product of -sum of Connected Graphs

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.

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.

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.

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.