ENUMERATION OF CONCRETE REGULAR COVERING PROJECTIONS

Counting covering spaces of graphs is one of the rapidly progressing a spects within the enumerative branch of topological graph theory. A co vering projection is said to be concrete if it is accompanied by an ex plicit partition of the vertex set of the covering graph into ''sheets '' such that each sheet meets each vertex fiber exactly once. The natu ral projection (subscript erasure) of the voltage graph construction i s the prototype of a concrete projection. An isomorphism of concrete c overing projections maps sheets to sheets. Polya and DeBruijn enumerat ive methods and Moebius inversion are used to derive a formula to coun t the isomorphism classes of regular covering projections of a graph.