A classification of 2-arc-transitive circulant digraphs
Let \(\mathbb{Z}_n\) denote the cyclic group of integers modulo \(n\), and \(S\) be a subset of \(\mathbb{Z}_n\setminus\{0\}\). A circulant digraph \(D_n(S)\) is a directed graph with vertex set \(\mathbb{Z}_n\) and the property that for all \(i,j\in\mathbb{Z}_n\) there is an arc from \(i\) to \(j\) iff \(j-i\in S\). A directed graph \(D\) is called 2-arc-transitive if and only if \(D\) is vertex transitive and \(\Aut(D)\) acts transitively on the set of 2-arcs of \(D\). The main result is a classification of all 2-arc-transitive circulant digraphs.
scientific article; zbMATH DE number 1506837