Abstract
Let F be a finite field, a positive integer, and the set consisting of all n × n matrices over F. The rank-decreasing graph of is a directed graph with vertex set , and there is a directed edge from to if and only if . In [Automorphism group of the rank-decreasing graph over the semigroup of upper triangular matrices, Comm. Algebra, 44(2016): 4088-4096], the authors described the automorphisms of the subgraph of induced by all upper triangular matrices in , and left the automorphisms of open. In this paper, we determine the automorphisms of .
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