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
q
d2
i
+ d2
j if the vertices vi and vj are
adjacent, and 0 otherwise. The spectral radius 1 and the energy Eso of Aso are examined. In particular,
upper bounds on Eso are obtained, as well as Nordhaus–Gaddumtype results for 1 and Eso.
1. Introduction