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 $\pi$-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.
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