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Isomorphism Classes of Concrete Graph Coverings
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Journal Article
Isomorphism Classes of Concrete Graph Coverings
1998
Overview
Hofmeister introduced the notion of a concrete (resp., concrete regular) covering of a graph G and gave formulas for enumerating the isomorphism classes of concrete (resp., concrete regular) coverings of G [Ars Combin., 32 (1991), pp. 121--127; SIAM J. Discrete Math., 8 (1995), pp. 51--61]. In this paper, we show that the number of the isomorphism classes of n-fold concrete (resp., concrete regular) coverings of G is equal to that of the isomorphism classes of n-fold (resp., regular) coverings of a new graph, the join$G+\\infty$of G and an extra vertex$\\infty$ . As a consequence, we can enumerate the isomorphism classes of concrete (resp., concrete regular) coverings of a graph by using known formulas for enumerating the isomorphism classes of coverings (resp., regular coverings) of a graph.
Publisher
Society for Industrial and Applied Mathematics
