【Key words】 embedding； weak embedding； strong embedding； joint tree； total genus distribution； genus distribution；
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The basic theory of my thesis is joint tree model for embedding which was created by Liu in 2003;The method used here is called surface generating method.
本文研究的基础是嵌入的联树模型，采用的是曲面生成法。
参考来源 - 三类字母图可定向嵌入亏格分布·2,447,543篇论文数据，部分数据来源于NoteExpress
在联树模型的基础上，把图在曲面上的嵌入用其联树，也即其关联曲面来表示。
On the basis of the joint tree model, an embedding of a graph on a surface can be rep-resented by a joint tree, further by an associated surface of it.
2003年刘提出的图的联树（1979的文章体现了这种思想）为嵌入亏格分布的研究提供了理论基础。
Liu created joint trees, initiated in his early paper in 1979, of a graph in 2003 which provided a foundation on studying embedding genus distribution.
在刘彦佩提出的联树法的基础上，通过分类一类新图类的可定向嵌入曲面求出了这类图类的可定向嵌入的亏格分布。
In this paper, We obtain the total genus polynomials for two new classes of 4-regular graphs by using the joint tree model of a graph embedding introduced by Yanpei Liu.
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