Automorphisms of the zero-divisor graph of the ring of all n x n matrices over a finite field

作者：Wang, Long^*

来源：Discrete Mathematics, 2016, 339(8): 2036-2041.

DOI：10.1016/j.disc.2016.02.021

• Digraphs
• Automorphisms of a graph
• Zero-divisor graphs

Let F-q be a finite field with q elements, Mat(n)(F-q) be the ring of all n x n matrices over F-q. The zero-divisor graph M of Mat(n)(F-q) is a digraph with vertex set of all nonzero zero-divisors of Mat(n)(F-q) 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 Mat(n)(F-q).

• 出版日期2016-8-6
• 单位安徽理工大学