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

2025/08/03 by Fateme Movahedi, Movahedi, F.
Computer Science · Mathematics · #05C09 #05C90 #05C92 #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2508.06531

openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider a simple graph G with vertex set V = \v₁, v₂, …, v_n\ and edge set E. The diminished Sombor matrix M_DS(G) is constructed such that its (i, j) entry is (√(d_i²+d_j²))/(d_i+d_j) if vertices v_iv_j ∈ 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.

Citations

• Diminished Sombor index and its relationship with topological indices
• On the Sombor characteristic polynomial and Sombor energy of a graph
• The Sombor index of trees and unicyclic graphs with given maximum degree
• On the spectral radius, energy and Estrada index of the Sombor matrix of graphs
• Graph theory and molecular orbitals. Total φ-electron energy of alternant hydrocarbons

Related

• On the spectral radius, energy and Estrada index of the Sombor matrix of graphs
• On the Sombor characteristic polynomial and Sombor energy of a graph
• Spectral properties of p-Sombor matrices and beyond
• Extremal trees, unicyclic and bicyclic graphs with respect to p-Sombor spectral radii
• On Euler-Sombor Energy of Graphs