On the spectral radius, energy and Estrada index of the Sombor matrix of graphs
نویسندگان
1 School of Mathematics, China University of Mining and Technology, 221116, Xuzhou, P. R. China
2 School of Mathematics, China University of Mining and Technology, 221116, Xuzhou, P. R. China
3 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
doi
10.22108/toc.2022.127710.1827چکیده
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.
