On spectrum of the zero-divisor graph of matrix ring

Krishnat Masalkar; Anil Khairnar; Anita Lande; Lata Kadam

paper

On spectrum of the zero-divisor graph of matrix ring

arXiv:2312.09934

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 $x y = 0$ or $y x = 0$ in $R$ . By using Weyl's inequality we give bounds on eigenvalues of adjacency matrix of $Γ (M_{2} (F))$ , where $M_{2} (F)$ is a $2 \times 2$ matrix ring over a finite field $F$ .