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

Document Type : Research Paper


1 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

2 School of Mathematics, China University of Mining and Technology, 221116, Xuzhou, P. R. China


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.


Main Subjects

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Volume 12, Issue 4 - Serial Number 4
December 2023
Pages 191-205
  • Receive Date: 08 March 2021
  • Revise Date: 03 September 2022
  • Accept Date: 07 September 2022
  • Published Online: 01 December 2023