Abstract
A graph is called s -regular if its automorphism group acts regularly on the set of its s -arcs. In this paper, the s -regular cyclic or elementary abelian coverings of the Petersen graph for each s ≥1 are classified when the fibre-preserving automorphism groups act arc-transitively. As an application of these results, all s -regular cubic graphs of order 10 p or 10 p 2 are also classified for each s ≥1 and each prime p , of which the proof depends on the classification of finite simple groups.
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