A classification of orientably-regular embeddings of complete multipartite graphs

  • Authors:

  • Shaofei Du;Jun-Yang Zhang

  • Affiliations:

  • -;-

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2014

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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) [1], James and Jones (1985) [14]. During the past twenty years, several papers such as Du et al. (2007, 2010) [8,9], Jones et al. (2007, 2008) [16,17], Kwak and Kwon (2005, 2008) [18,19] and Nedela et al. (1997, 2002) [22,23] contributed to the orientably-regular embeddings of complete bipartite graphs K"2"["n"] and the final classification was given by Jones [15] in 2010. Based on our former paper (Zhang and Du, 2012) [24], this paper gives a complete classification of orientably-regular embeddings of graphs K"m"["n"] for the general cases m=3 and n=2.