Enumerating regular graph coverings whose covering transformation groups are ℤ_2-extensions of a cyclic group

Abstract

Several types of the isomorphism classes of graph coverings have been enumerated by many authors. In 1988, Hofmeister enumerated the double covers of a graph, and this work was extended to n -fold coverings of a graph by the second and third authors. For regular coverings of a graph, their isomorphism classes were enumerated when the covering transformation group is a finite abelian or dihedral group. In this paper, we enumerate the isomorphism classes of graph coverings when the covering transformation group is a ℤ 2 -extension of a cyclic group, including generalized quaternion and semi-dihedral groups.