  Cycle prefix digraphs have been proposed as an efficient model of symmetric
interconnection networks for parallel architecture. It has been discovered that
the cycle prefix networks have many attractive communication properties. In
this paper, we determine the automorphism group of the cycle prefix digraphs.
We show that the automorphism group of a cycle prefix digraph is isomorphic to
the symmetric group on its underlying alphabet. Our method can be applied to
other classes of graphs built on alphabets including the hypercube, the Kautz
graph,and the de Bruijn graph.
