Enumerating regular graph coverings whose covering transformation groups are ℤ2-extensions of a cyclic group

Jian-Bing Liu, Jaeun Lee, Jin Ho Kwak

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 ℤ2-extension of a cyclic group, including generalized quaternion and semi-dihedral groups.


Keywords


Graphs, regular coverings, voltage assignments, enumeration, Möbius functions (on a lattice), group extensions

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DOI: https://doi.org/10.26493/1855-3974.1419.3e9

ISSN: 1855-3974

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