Quotients of connected regular graphs of even degree

This paper introduces a method of listing all nonequivalent quotients of any connected regular graph of even degree with a given 2-factorization. The method is based on the characterization of connected 2d-regular graphs as Schreier coset graphs given by Gross (J. Combin. Theory Ser. B22 (1977), 227–232). Various representations of a given graph with a fixed 2-factorization are also investigated. The work is related to graph imbedding theory, particularly to voltage and current graphs.