\(s\)-regular cyclic coverings of the three-dimensional hypercube \(Q_{3}\).
An \(s\)-regular graph is a graph with an automorphism group acting regularly on the set of \(s\)-arcs. The main result of the paper is the following theorem: Let \(\widetilde X\) be a connected cyclic covering of the 3-dimensional hypercube \(Q_3\) and let the group of fibre-preserving automorphisms of \(\widetilde X\) act arc-transitively. Then, \(\widetilde X\) is either 1-regular or 2-regular. Furthermore the isomorphism classes of all 1-regular and 2-regular graphs \(\widetilde X\) are listed.
scientific article; zbMATH DE number 1970588