A note on automorphisms of the zero-divisor graph of upper triangular matrices

摘要

Let F-q be a finite field with q elements, n(>= 3) a positive integer, T (n, q) the set of all n x 77, upper triangular matrices over F-q. In [13], the zero-divisor graph of T(n, q), written as T, is defined to be a graph with all nonzero zero-divisors in T(n, q) as vertices, and there is a directed edge from a vertex X to a vertex Y if and only if XY = 0. The subgraph of T induced by all rank one matrices in T (n, q) is denoted by R. Wong et al. (2014) in [13] determined the automorphisms of R. and left the automorphisms of T unsolved. In this note, we solve this problem. (C) 2014 Elsevier Inc. All rights reserved.