%0 Journal Article
%T On the spectral radius, energy and Estrada index of the Sombor matrix of graphs
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Lin, Zhen
%A Zhou, Ting
%A Miao, Lianying
%D 2023
%\ 12/01/2023
%V 12
%N 4
%P 191-205
%! On the spectral radius, energy and Estrada index of the Sombor matrix of graphs
%K Sombor matrix
%K Sombor spectral radius
%K Sombor energy
%K Sombor Estrada index
%R 10.22108/toc.2022.127710.1827
%X 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.
%U https://toc.ui.ac.ir/article_26896_ab1f533d12c78afa9542037d171aed60.pdf