On spectrum of the zero-divisor graph of matrix ring

2023/12/15 by Krishnat Masalkar, Masalkar, Krishnat, Anil Khairnar +5
Computer Science · Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Matrix Theory and Algorithms #Primary 05C25 #Rings, Modules, and Algebras #Secondary 05C50 #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2312.09934

openalex publication_date 2023/12/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a ring R, the zero-divisor graph is a simple graph Γ(R) whose vertex set is the set of all non-zero zero-divisors in a ring R, and two distinct vertices x and y are adjacent if and only if xy=0 or yx=0 in R. By using Weyl's inequality we give bounds on eigenvalues of adjacency matrix of Γ(M₂(F)), where M₂(F) is a 2 × 2 matrix ring over a finite field F.

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