On Sombor indices of generalized tensor product of graph families

Abstract

Graph invariants are extensively being used in different fields for analysing the structural properties of different compounds. Several topological indices, their properties and relations between different indices have been explored. Ivan Gutman recently introduced a new topological index, based on the vertex degree, termed as Sombor indices in the field of Chemical Graph theory. It is based on the Eulerian (distance) metric. Sombor indices and its properties have been explored on a wide range of graphs. However, the existing literature of graph theory bears fewer exploration in the analysis of topological indices of product graphs, a significant operation on graphs. Studying the topological features of molecular paths and cycles is vital for understanding chemical compounds, offering key insights into their structures and behaviours, benefiting diverse sectors such as drug discovery, material science, and chemical engineering. With this motivation, the Sombor indices of tensor product and 2-tensor product of certain families of graphs are established in this paper. Some of these product graphs are analysed by means of SO based graphical entropy.

Keywords

• Sombor index
• Tensor graph products
• 2-tensor graph products
• Graph entropy
• Regular graph
• Bi-regular graph