Regular embeddings of complete bipartite graphs: classification and enumeration
نویسندگان
چکیده
منابع مشابه
Regular embeddings of complete bipartite graphs: classification and enumeration
The regular embeddings of complete bipartite graphs Kn,n in orientable surfaces are classified 5 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 fa...
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A 2-cell embedding of a graph G into a closed (orientable or nonorientable) surface is called regular if its automorphism group acts regularly on the flags mutually incident vertex-edge-face triples. In this paper, we classify the regular embeddings of complete bipartite graphs Kn,n into nonorientable surfaces. Such a regular embedding of Kn,n exists only when n = 2p a1 1 p a2 2 · · · p ak k (a...
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If G = (V,E) is a graph, the incidence graph I(G) is the graph with vertices V ∪ E and an edge joining v ∈ V and e ∈ E when and only when v is incident with e in G. For G equal to Kn (the complete graph on n vertices) or Kn,n (the complete bipartite graph on n+ n vertices), we enumerate the matchings (sets of edges, no two having a vertex in common) in I(G), both exactly (in terms of generating...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2010
ISSN: 0024-6115
DOI: 10.1112/plms/pdp061