On the spectral radius, energy and Estrada index of the Sombor matrix of graphs

Let G be a simple undirected graph with vertex set V(G)=\{v_1, v_2,\ldots,v_n\} and edge set E(G). The Sombor matrix \mathcal{S}(G) of a graph G is defined so that its (i,j)-entry is equal to \sqrt{d_i^2+d_j^2} if the vertices v_i and v_j are adjacent, and zero otherwise, where d_i denotes the degree of vertex v_i in G. In this paper, lower and upper bounds on the spectral radius, energy and Estrada index of the Sombor matrix of graphs are obtained, and the respective extremal graphs are characterized.

On the spectral radius, energy and Estrada index of the Sombor matrix of graphs Keywords:

Sombor matrix , Sombor spectral radius , Sombor energy , Sombor Estrada index