University of IsfahanTransactions on Combinatorics2251-865712420231201On the spectral radius, energy and Estrada index of the Sombor matrix of graphs1912052689610.22108/toc.2022.127710.1827ENZhenLinSchool 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. ChinaTingZhouSchool of Mathematics, China University of Mining and Technology, 221116, Xuzhou, P. R. ChinaLianyingMiaoSchool of Mathematics, China University of Mining and Technology, 221116, Xuzhou, P. R. ChinaJournal Article20210308Let $G$ 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