Abstract
A graph is s-regular if its automorphism group acts regularly on the set of its s-arcs. An infinite family of cubic 1-regular graphs was constructed in [7] as cyclic coverings of the three-dimensional Hypercube, and a classification of all s-regular cyclic coverings of the complete bipartite graph of order 6 was given in [8] for each s≥1, whose fibre-preserving automorphism subgroups act arc-transitively. In this paper, the authors classify all s-regular dihedral coverings of the complete graph of order 4 for each s≥1, whose fibre-preserving automorphism subgroups act arc-transitively. As a result, a new infinite family of cubic 1-regular graphs is constructed.
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