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arXiv · 0911.4340

Regular embeddings of complete bipartite graphs: classification and enumeration

Gareth A. Jones
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Abstract

The regular embeddings of complete bipartite graphs $K_{n,n}$ in orientable surfaces are classified and enumerated, and their automorphism groups and combinatorial properties are determined. The method depends on earlier classifications in the cases where $n$ is a prime power, obtained in collaboration with Du, Kwak, Nedela and Škoviera, together with results of Itô, Hall, Huppert and Wielandt on factorisable groups and on finite solvable groups.

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Gareth A. Jones. 2009-11-23. Regular embeddings of complete bipartite graphs: classification and enumeration. https://doi.org/10.1112/plms%2Fpdp061

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