Enumeration of Concrete Regular Covering Projections
Michael Hofmeister · SIAM Journal on Discrete Mathematics · 1995
Counting covering spaces of graphs is one of the rapidly progressing aspects within the enumerative branch of topological graph theory. A covering projection is said to be concrete if it is accompanied by an explicit partition of the vertex set of the covering graph into “sheets” such that each sheet meets each vertex fiber exactly once. The natural projection (subscript erasure) of the voltage graph construction is the prototype of a concrete projection. An isomorphism of concrete covering projections maps sheets to sheets. Pólya and DeBruijn enumerative methods and Moebius inversion are used to derive a formula to count the isomorphism classes of regular covering projections of a graph.