Sombor Index Under Some Graph Products

Abstract

‎Let G=(V‎, ‎E) be a graph with vertex set V(G) and edge set E(G)‎. ‎The Sombor index of a graph G‎, ‎SO(G)‎, ‎is defined as ∑uv∈ E(G) √(d2u+d2v), ‎where du is the degree of vertex u in V(G)‎. ‎In the present paper‎, ‎we determine the lower bound for the Sombor index of edge corona‎, ‎R-edge and R-vertex corona products of two graphs‎. ‎We also compute the exact value for the Sombor index of the line graphs of subdivision of tadpol‎, ‎ladder and wheel graphs‎.

Keywords

• sombor index
• edge corona
• r-vertex corona
• line graphs
• subdivision of tadpole graph