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

Zhen Lin

paper

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

arXiv:2102.03960

Abstract

Let $G$ be a simple undirected graph with vertex set $V (G) = {v_{1}, v_{2}, \dots, v_{n}}$ and edge set $E (G)$ . The Sombor matrix $S (G)$ of a graph $G$ is defined so that its $(i, j)$ -entry is equal to $d_{i}^{2} + d_{j}^{2}$ 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.

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