A note on automorphisms of the zero-divisor graph of upper triangular matrices
A note on automorphisms of the zero-divisor graph of upper triangular matrices
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DOI：
10.1016/j.laa.2014.09.035
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发表时间：
2015-01
影响因子：
1.1
通讯作者：
Long Wang
中科院分区：
文献类型：
--
作者：
Long Wang
设Fq是q元有限域，n（≥ 3）为正整数，T（n，q）为Fq上所有n× n上三角矩阵的集合.在文献[13]中，T（n，q）的零因子图被定义为以T（n，q）中的所有非零零因子为顶点的图，并且存在从顶点X到顶点Y的有向边当且仅当XY = 0。由T（n，q）中所有秩一矩阵导出的T的子图记为R。Wong等人（2014）在[13]中确定了R的自同构，并留下了T的自同构未解。在本文中，我们解决了这个问题。
Let F q be a finite field with q elements, n (≥ 3) a positive integer, T (n, q) the set of all n× n 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 X Y= 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.