Automorphism Group of the Rank-decreasing Graph Over the Semigroup of Upper Triangular Matrices

作者：Wang, Dengyin^*; Ma, Xiaobin; Tian, Fenglei

来源：Communications in Algebra, 2016, 44(9): 4088-4096.

DOI：10.1080/00927872.2015.1087017

• Directed graphs
• Graph automorphisms
• Zero-divisor graphs

Let F-q be a finite field with q elements, n2 a positive integer, and T(n, q) the semigroup of all nxn upper triangular matrices over F-q. The rank-decreasing graph ? of T(n, q) is a directed graph which has T(n, q) as vertex set, and there is a directed edge from AT(n, q) to BT(n, q) if and only if r(AB)<r(B). The zero-divisor graph of T(n, q), with vertex set of all nonzero zero-divisors of T(n, q) and there is a directed edge from a vertex A to a vertex B if and only if AB=0, can be viewed as a subgraph of ?. In [16], L. Wang has determined the automorphisms of the zero-divisor graph of T(n, q). In this article, by applying the main result of [17] we determine the automorphisms of the rank-decreasing graph ? of T(n, q).

• 出版日期2016
• 单位中国矿业大学（北京）