一些完全图三边形嵌入个数的研究
首发时间：2018-04-09
摘要：完全图Kn 在可定向曲面上有三边形嵌入，当且仅当n ≡ 0, 3, 4, 7(mod12)。这篇文章主 要研究了完全图K12s+4 和K12s+7 的可定向三边形嵌入的个数问题。Luis Goddyn 利用路的优 美标号和电流图理论给出了完全图K12s+7 在可定向曲面上的不同构的三边形嵌入的个数至少 是11s，本文给出了完全图K12s+7 的电流图的一种新的电流标号方法。Vladimir P.Korzhik 根 据电流图理论给出了完全图K12s+4 在可定向曲面上的不同构的三边形嵌入的个数至少是4s， 本文通过路的双优美标号和电流图理论，以及电流图的一旋系统的个数，提高了完全图K12s+4 的不同构的可定向三边形嵌入个数的下界。
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On the number of triangular embeddings of some complete graphs
Abstract：It is known that a complete graph Kn, has an orientable triangular embedding if and only if n ≡ 0, 3, 4, 7(mod12). In this paper, we study the number of non-isomorphic oriented triangular embeddings of K12s+4 和K12s+7. According to graceful labellings and current graph theory of the path graph, Luis Goddyn, et al, proved there are at least 11s non-isomorphic oriented triangular embeddings of K12s+7. In this paper, we find a new current labeling method for the current graph of K12s+7. According to current graph theory, Vladimir P.Korzhik showed there are at least 4s non-isomorphic oriented triangular embeddings of K12s+4. In this paper, according to double graceful labeling of path graph and the number of one-rotation systems for the current graph, we improve the lower bound for the number of triangular embeddings of K12s+4.
Keywords： embedding minimum genus current graph K12s+7
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