On Sombor Energy of Graphs with self-loops

Abstract

The goal of this paper is to broaden the concept of Sombor Energy from a simple graph to one containing self-loops. Let G be a simple nth-order graph, and  be the graph generated by adding  self-loops to G. Sombor matrix of  is defined as

If  are eigenvalues of , then Sombor Energy of  is defined as

 where  is the degree of vertex with self loop