On characteristic polynomial and energy of Sombor matrix

Let G be a simple graph with vertex set V = { v 1 , v 2 , … , v n } , and let d i be the degree of the vertex v i . The Sombor matrix of G is the square matrix A S O of order n , whose ( i , j ) -element is √ d 2 i + d 2 j if v i and v j are adjacent, and zero otherwise. We study the characteristic polynomial, spectrum, and energy of A S O . A few results for the coefficients of the characteristic polynomial, and bounds for the energy of A S O are established.