Arc-Transitive Dihedral Regular Covers of Cubic Graphs

Jicheng Ma

Abstract


A regular covering projection is called dihedral or abelian if the covering transformation group is dihedral or abelian. A lot of work has been done with regard to the classification of arc-transitive abelian (or elementary abelian, or cyclic) covers of symmetric graphs. In this paper, we investigate arc-transitive dihedral regular covers of symmetric (arc-transitive) cubic graphs. In particular, we classify all arc-transitive dihedral regular covers of $K_4$, $K_{3,3}$, the 3-cube $Q_3$ and the Petersen graph.


Keywords


Arc-transitive graph; Regular cover; Dihedral cover; Cubic graph

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