Sombor Index over the Tensor and Cartesian Products of Monogenic Semigroup Graphs

Abstract

Consider a simple graph G with vertex set V(G) and edge set E(G). A graph invariant for G is a number related to the structure of G, which is invariant under the symmetry of G. The Sombor index of G is a new graph invariant defined as SO(G)=∑uv∈E(G)(du)2+(dv)2. In this work, we connected the theory of the Sombor index with abstract algebra. We computed this topological index over the tensor and Cartesian products of a monogenic semigroup graph by presenting two different algorithms; the obtained results are illustrated by examples.