Automorphisms of the zero-divisor graph over 2 × 2 matrices

Abstract

The zero-divisor graph of a noncommutative ring R, denoted by Γ(R), is a graph whose vertices are nonzero zero-divisors of R, and there is a directed edge from a vertex x to a distinct vertex y if and only if xy = 0. Let R = M2(Fq) be the 2×2 matrix ring over a finite field Fq. In this article, we investigate the automorphism group of Γ(R).