A Classification of Orientable Regular Embeddings of Complete Multipartite Graphs

2012/02/09 by Shaofei Du, Du, Shaofei, Junyang Zhang +1
Mathematics · #05C25 #05E30 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C25 #msc:05E30 #msc:20B25

paper · pdf · doi:10.48550/arxiv.1202.1974

20 pages

arxiv created 2012/06/10 · arxiv updated 2012/06/12

Abstract

Let K_m[n] be the complete multipartite graph with m parts, while each part contains n vertices. The orientably-regular embeddings of complete graphs K_m[1] have been determined by Biggs (1971) \citeBig1, James and Jones (1985) \citeJJ. During the past twenty years, several papers such as Du et al.(2007, 2010) \citeDJKNS1,DJKNS2, Jones et al. (2007, 2008) \citeJNS1,JNS2, Kwak and Kwon (2005, 2008) \citeKK1,KK2 and Nedela et al. (1997, 2002)\citeNS,NSZ contributed to the orientably-regular embeddings of complete bipartite graphs K_2[n] and the final classification was given by Jones \citeJon1 in 2010. Based on our former paper \citeZD, this paper gives a complete classification of orientably-regular embeddings of graphs K_m[n] for the general cases m≥ 3 and n≥ 2.

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