Sharp Bounds on the Sombor Energy of Graphs

For a simple graph G with vertex set {v1, v2, . . ., vn} and edge set E(G). The Sombor matrix S(G) of G is an n × n matrix, whose (i, j)-entry is equal is ^q d²_i + d²_j, if i and j are adjacent and 0, otherwise. The multi-set of the eigenvalues of S(G) is known as the Sombor spectrum of G, denoted by µ1 ≥ µ2 ≥ · · · ≥ µn, where µ1 is the Sombor spectral radius of G. The absolute sum of the Sombor eigenvalues if known as the Sombor energy. In this article, we find the bounds for the Sombor energy of G and characterize the corresponding extremal graphs. These bounds are better than already known results on Sombor energy.