Abstract
In this paper, we classify some reflexible edge-transitive orientable embeddings of complete bipartite graphs. As a by-product, we classify groups Γ such that (i) Γ = XY for some cyclic groups X = ⟨ x ⟩ and Y = ⟨ y ⟩ with X ∩ Y = {1 Γ } and (ii) there exists an automorphism of Γ which sends x and y to x −1 and y −1 , respectively.
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