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Abstract
Let F
q
be a finite field with q elements, n(≥2) a positive integer, and T
n
(q) the semigroup of all n × n upper triangular matrices over F
q
. The generalized Cayley graph GCay(T
n
(q)) of T
n
(q) is a directed graph with vertex set T
n
(q), in which there is a directed edge from a vertex A to a distinct vertex B if and only if B = XAY for some X, Y ∈ T
n
(q). The main result of this article proves that a bijective map σ is an automorphism of GCay(T
n
(q)) if and only if, for any vertex A of GCay(T
n
(q)), either σ(A) = P
A
AQ
A
or σ(A) = P
A
JA
t
JQ
A
, where A
t
denotes the transpose of A, , and P
A
and Q
A
are invertible upper triangular matrices depending on A.
ACKNOWLEDGMENT
The authors are grateful to the referee for his (or her) valuable comments, corrections, and suggestions, which make the article more readable.
Notes
Communicated by M. Bresar.