Automorphism groups of k-arc transitive covers Original Research Article

A directed graph is k-arc transitive if it has an automorphism group which acts transitively on the set of k-arcs. Several techniques have been proposed in the literature to construct k-arc transitive digraphs for each positive integer k and each degree r of regularity. Following previous work by the authors, we study the full automorphism group of k-arc transitive digraphs and we give its structure for digraphs of degree 2. We describe the k-transitive coverings of complete digraphs which can be obtained by the construction technique introduced by the authors in previous work. Finally, we provide examples of k-arc transitive digraphs which are non-homomorphic to a cycle.