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摘要: 令Cm,n表示长为m的圈与n个孤立点的联结(join)所得的图. 本文证明了Cm,n的最小亏格和最小不可定向亏格与完全二部图Km,n的相等. 同时，证明当m≥2并且n≥2时, Km,n在其最小可定向曲面上有一个强嵌入; 当m≥3并且n≥3,时, 在最小不可定向曲面上有一个强嵌入.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.
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Key words:
- genusnonorientable genusstrong embedding /
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