Counting some finite-fold coverings of a graph
A graph \(\widetilde G\) is called a covering of the graph \(G\) with the projection \(p:\widetilde G\to G\) iff there is a surjection \(p:V(\widetilde G)\to V(G)\) such that \(p|_{N(\tilde v)}:N(\tilde v)\to N(v)\) is a bijection for any vertex \(v\in V(G)\) and \(\tilde v\in p^{-1}(v)\). If the covering projection \(p\) is \(n\)-to-one the covering is said to be \(n\)-fold. \textit{D. A. Waller} [Bull. Aust. Math. Soc. 14, 233-248 (1976; Zbl 0318.05113)] and \textit{M. Hofmeister} [J. Graph Theory 12, No. 3, 437-444 (1988; Zbl 0649.05036)] counted the number of isomorphism classes of double coverings of a given graph \(G\). Here the general case is investigated.
scientific article; zbMATH DE number 93443