University of Isfahan Transactions on Combinatorics 2251-8657 12 4 2023 12 01 On the spectral radius, energy and Estrada index of the Sombor matrix of graphs 191 205 26896 10.22108/toc.2022.127710.1827 EN Zhen Lin School of Mathematics and Statistics, Qinghai Normal University, 810008, Xining, P. R. China The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, 810008, Xining, P. R. China Ting Zhou School of Mathematics, China University of Mining and Technology, 221116, Xuzhou, P. R. China Lianying Miao School of Mathematics, China University of Mining and Technology, 221116, Xuzhou, P. R. China Journal Article 2021 03 08 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. https://toc.ui.ac.ir/article_26896_ab1f533d12c78afa9542037d171aed60.pdf