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Classification of reflexible edge-transitive embeddings of Km,n for odd m,n
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In this paper, we classify reflexible edge-transitive embeddings of complete bipartite graphs Km,n for any odd positive integers m and n. As a result, for any odd m,n, it will be shown that there exists only one reflexible edge-transitive embedding of Km,n up to isomorphism.
Abstract
In this paper, we classify reflexible edge-transitive embeddings of complete bipartite graphs Km,n for any odd positive integers m and n. As a result, for any odd m,n, it will be shown that there exists only one reflexible edge-transitive embedding of Km,n up to isomorphism.
참고문헌 (9)
- S. F. Du, "Regular embeddings of Kn;n where n is a power of 2. I: Metacyclic case", Europ. J. Combinatorics, 28(6), pp.1595~1609 (2007)
- S. F. Du, "Regular embeddings of Kn;n where n is a power of 2", II: Non-metacyclic case, submitted, ~
- G. A. Jones, "Regular embeddings of complete bipartite graphs: classi cation and enu- meration", submitted, ~
- G. Jones, "Complete bipartite graphs with a unique regular embedding", J. Combin. Theory Ser. B, 98(2), pp.241~248 (2008)
- G. Jones, "Regular embeddings of Kn;n where n is an odd prime power", Europ. J. Combinatorics, 28(6), pp.1863~1875 (2007)
- J. H. Kwak, "Regular orientable embeddings of complete bipartite graphs", J. Graph Theory, 50(2), pp.105~122 (2005)
- J. H. Kwak, "Classi cation of re exible regular embeddings and self-Petrie dual regular embeddings of the complete bipartite graphs", Discrete Math, 308(11), pp.2156~2166 (2008)
- J. H. Kwak, "Classi cation of nonorientable regular embeddings of com-plete bipartite graphs", submitted, ~
- R. Nedela, "Regular embedding of complete bipartite graphs", Disc. Math, 258, pp.379~381 (2002)
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