On sombor energy of graphs

Abstract

The concept of Sombor index SO(G) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by SO(G). This paper introduces a new matrix for a graph G, called the Sombor matrix, and defines a new variant of graph energy called Sombor energy ES(G) of a graph G. The striking feature of this new matrix is that it is related to well-known degree-based topological indices called forgotten indices. When ES(G) values of some molecules containing hetero atoms are correlated with their total π-electron energy, we got a good correlation with the correlation coefficient r = 0.976. Further, we found some bounds and characterizations on the largest eigenvalue of S(G) and Sombor energy of graphs.