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

AbstractThe 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

Symmetry Parameters of Two-Generator Circulant Graphs

The derived graph of a voltage graph consisting of a single vertex and two loops of different voltages is a circulant graph with two generators. We characterize the automorphism groups of connected, two-generator circulant graphs, and give their determining and distinguishing number, and when relevant, their cost of 2-distinguishing. We do the same for the subdivisions of connected, two-generator circulant graphs obtained by replacing one loop in the voltage graph with a directed cycle