An infinite family of cubic one-regular graphs with unsolvable automorphism groups. (Q1402085)

A graph \(X\) is said to be vertex-transitive, edge-transitive, and arc-transitive if its automorphism group \(\Aut(X)\) is transitiv on the vertex set, edge set and arc set, respectively. A graph is said to be one-regular if \(\Aut(X)\) acts freely and transitively on the set of arcs. The first cubic one-regular graph was constructed by Frucht in 1952. Since then there is a large number of generalizations of this result. In this paper, an infinite family of cubic one-regular graphs with solvable automorphism group is constructed.