Spectral Radius and Energy of Sombor Matrix of Graphs

Abstract

Let G be a graph of order n. For i = 1, 2,…, n, let di be the degree of the vertex vi of G. The Sombor matrix Aso of G is defined so that its (i, j)-entry is equal to √d2i+d2j if the vertices vi and vj are adjacent, and 0 otherwise. The spectral radius ɳ1 and the energy Eso of Aso are examined. In particular, upper bounds on Eso are obtained, as well as Nordhaus-Gaddum-type results for ɳ1 and Eso.