Comparing Energy and Sombor Energy - An Empirical Study

Abstract

The Sombor index is a recently invented vertex-degree-based topological index, to which a matrix – called Sombor matrix – is associated in a natural manner. The graph energy E(G) is the sum of absolute values of the eigenvalues of the adjacency matrix of the graph G. Analogously, the Sombor energy ESO(G) is the sum of absolute values of the eigenvalues of the Sombor matrix. In this paper, we present computational results on the relations between ESO(G) and E(G) for various classes of (molecular) graphs, and establish the respective regularities. The correlation between ESO(G) and E(G) if found to be much more perplexed than earlier reported.