Abstract
Denote by C,(S) the circulant digraph with vertex set Z,, = {0,1,2,. n−1} and symbol set S(≠-S)⊆∖{0}. Let X be the automorphism group of C n (.S) and X,, the stabilizer of 0 in X. ThenCn(S) is arc-transitive if and only if Xoacts transitively onS. In this paper, Cn(S) with Xo|s being the symmetric group is characterized by its symbol set. By the way all the arctransitive circulant digraphs of degree 2 and 3 are given.
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