完全图K12s+10的最小亏格嵌入个数估计
首发时间:2018-03-30
摘要:拓扑图论的一个主要研究内容是将一个给定图G嵌入到一个特定的2-维闭曲面S(可定向曲面或不可定向曲面)上,使得该图中任意两条边仅于顶点处相交且每一个面都同胚于一个开圆盘.设fi:G!S(i=1;2)为图G在曲面S上的两个不同嵌入,如果存在图G的一个自同构 和曲面S的一个同胚映射h,满足关系式h(f1(G))=f2( (G)),则称嵌入f1和f2是同构的.图G的所有曲面嵌入中,最小的曲面亏格称为图G的最小亏格.本文借助路径的优美标号和电流图等相关理论,估计出完全图K12s+10至少有3G(s+1)×23s+1个(G(s+1)为路径P2s+1左端点标号被限制为固定值s+1的优美标号的个数)不同构的最小亏格嵌入.
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On the Number of the Minimum Genus Embedding for the Complete Graph K12s+10
Abstract:Topological graph theory mainly studies the embedding of a graph in surfaces(orientable surfaces and non-orientable surfaces), so that any of its two edges intersect only at the vertices, and each face is homeomorphic to an open disk. The genus of a graph is a kernel parameter of the topological graph theory, our paper focuses on the minimum genus embedding for the complete graphs. Two embeddings fi:G→S(i=1,2) of G in a surface S are considered as isomorphic, if there is a homemorphism of h:S→S and an automorphism ψof G such that h(f1(G)) =f2(ψ(G)). In this paper, we try to estimate the number of minimum genus embeddings for complete graphs of K12s+10 with the aid of the graceful labeling of the path graph and the current graph theory.
Keywords: complete graph minimal genus embedding graceful labelling current graph
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