Journal of East China Normal University(Natural Sc ›› 2011, Vol. 2011 ›› Issue (2): 17-21.

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Genus of Cm,n and strong genus embedding of Km,n

SHAN Song-ling, REN Han   

  1. Department of Mathematics, East China Normal University, Shanghai 200241, China
  • Received:2010-07-01 Revised:2010-10-01 Online:2011-03-25 Published:2011-03-25
  • Contact: SHAN Song-ling

Abstract: Let Cm,n be the join graph of Cm(a cycle of ength m) and n isolated vertices. In this paper, we first show hat the genus and nonorientable genus of Cm,n equal those of Km,n, which were well known and discovered by Ringel [1, 2].
Then we show that the complete bipartite graph Km,n has a strong orientable genus embedding if m≥2 and n≥2 and has a strong nonorientable genus embedding if m≥3 and n≥3.

Key words: nonorientable genus, strong embedding, genus, nonorientable genus, strong embedding

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