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NANOSYSTEMS: PHYSICS, CHEMISTRY, MATHEMATICS, 2021, 12 (4), P. 411–417

On Sombor energy of graphs

K. J. Gowtham – Dept. of Mathematics, University College of Science, Tumkur University, Tumakuru, Karnataka State, Pin 572 103, India; gowtham_k_j@yahoo.com
Narahari Narasimha Swamy – Dept. of Mathematics, University College of Science, Tumkur University, Tumakuru, Karnataka State, Pin 572 103, India; narahari_nittur@yahoo.com

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.

Keywords: Sombor index, Sombor energy, forgotten index.

DOI 10.17586/2220-8054-2021-12-4-411-417

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