The automorphism group of zero-divisor graph of a finite semisimple ring

Abstract

Let be a finite ring. The zero-divisor graph of written as is a digraph with vertex set the set of all nonzero zero-divisor of and for (needless distinct) there exists a directed edge from x to y if and only if xy = 0. The automorphism group of for a full matrix ring was characterized, and that for a finite semisimple ring remains open. In this article, we describe the automorphism group of when is a finite semisimple ring or a block upper triangular matrix ring over a finite field.Communicated by Peter Sin