Automorphisms of the zero-divisor graph of the ring of all [formula omitted] matrices over a finite field

Abstract

Let Fq be a finite field with q elements, Matn(Fq) be the ring of all n×n matrices over Fq. The zero-divisor graph M of Matn(Fq) is a digraph with vertex set of all nonzero zero-divisors of Matn(Fq) and there is a directed edge from a vertex A to a vertex B if and only if AB=0. In this paper, by applying the main result obtained in [20, Lin. Alg. Appl., 463(2014) 214-220], where the automorphisms of the subgraph of M induced by all rank one upper triangular matrices are determined, we determine the automorphisms of the zero-divisor graph M of Matn(Fq).