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Enumerating regular graph coverings whose covering transformation groups are \(\mathbb{Z}_2\)-extensions of a cyclic group. (English) Zbl 1404.05085

Summary: Several types of the isomorphism classes of graph coverings have been enumerated by many authors. M. Hofmeister [J. Graph Theory 12, No. 3, 437–444 (1988; Zbl 0649.05036)] 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 \(\mathbb{Z}_2\)-extension of a cyclic group, including generalized quaternion and semi-dihedral groups.

MSC:

05C30 Enumeration in graph theory
20F28 Automorphism groups of groups
20K27 Subgroups of abelian groups

Citations:

Zbl 0649.05036
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References:

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