Isomorphism classes of concrete graph coverings

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 + infinity of G and an extra vertex infinity. 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.open118sciescopu