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 \(\mathcal E(G)\) is the sum of absolute values of the eigenvalues of the adjacency
matrix of the graph \(G\). Analogously, the Sombor energy \(\mathcal E_{SO}(G)\) is the sum of absolute values of the eigenvalues of the Sombor matrix. In this paper, we present computational results on the relations between \(\mathcal
E_{SO}(G)\) and \(\mathcal E(G)\) for various classes of (molecular) graphs, and establish the respective regularities. The correlation between \(\mathcal E_{SO}(G)\) and \(\mathcal E(G)\) if found to be much more perplexed than earlier
reported.
