Diminished Sombor matrix, spectral radius, and energy of the graphs

F. Movahedi

paper

Diminished Sombor matrix, spectral radius, and energy of the graphs

arXiv:2508.06531

Abstract

Consider a simple graph $G$ with vertex set $V = {v_{1}, v_{2}, \dots, v_{n}}$ and edge set $E$ . The diminished Sombor matrix $M_{D S} (G)$ is constructed such that its $(i, j)$ entry is $\frac{d _{i}^{2} + d _{j}^{2}}{d _{i} + d _{j}}$ if vertices $v_{i} v_{j} \in E$ , and $0$ otherwise, where $d_{i}$ represents the degree of vertex $v_{i}$ . In this paper, we establish sharp bounds for the spectral radius, and energy of the Sombor matrix of graphs and identify the graphs that attain these extremal values.