On automorphisms of circulant digraphs on pm vertices, p an odd prime Original Research Article

The circulant digraph Γ is considered when the number n of vertices of Γ is equal to pm for an odd prime p. The main results are an implicit characterization of the groups Aut(Γ) in the general case, and an explicit characterization in the case n=p4. The argument is based on spectral techniques and classical constructions of permutation groups.