Zhen Lin - School of Mathematics and Statistics, Qinghai Normal University, ۸۱۰۰۰۸, Xining, P. R. China The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, ۸۱۰۰۰۸, Xining, P. R. China
Ting Zhou - School of Mathematics, China University of Mining and Technology, ۲۲۱۱۱۶, Xuzhou, P. R. China
Lianying Miao - School of Mathematics, China University of Mining and Technology, ۲۲۱۱۱۶, Xuzhou, P. R. China

Let G be a simple undirected graph with vertex set V(G)=\{v_۱, v_۲,\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^۲+d_j^۲} 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.

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