The energy and sombor index of graphs

Abstract

The energy of a graph is defined to be the sum of absolute values of eigenvalues of its adjacency matrix. The Sombor index of a graph is a novel topological index of a graph. In this paper, we study relations between energy and Sombor index of a graph G in terms of its degrees. Moreover, we give upper bound for a regular graph in terms of its Sombor index.