Published online by Cambridge University Press: 17 April 2009
Two 2-cell embeddings i, j of a graph G into surfaces and ′ are said to be congruent with respect to a subgroup Γ of Aut(G) if there are a homeomorphism h: → ′ and an automorphism γ ∈ Γ such that h ∘ i = j ∘ γ. In this paper, we compute the total number of congruence classes of 2-cell embeddings of any bouquet of circles into surfaces with respect to a group consisting of graph automorphisms of a bouquet.