Abstract
A graph is s- regular if its automorphism group acts regularly on the set of s-arcs. An infinite family of cubic 1-regular graphs was constructed in European J. Combin. 23 (2002) 559, as cyclic coverings of the three-dimensional hypercube Q 3. In this paper, we classify the s-regular cyclic coverings of Q 3 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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