曲面上完全映射的个数
The Number of Complete Maps on Surfaces
摘要：
映射是胞腔嵌入曲面的连通拓扑图，完全映射是胞腔嵌入曲面的完全图。本文证明了n阶完全映射的所有自同构都是由其顶点上的置换决定的。应用一个在给定基础图的曲面上计数映射的方案，得到了可定向曲面和非可定向曲面上无根完全映射的个数。
英文摘要：
A map is a connected topological graph cellularly embedded in a surface and a complete map is a cellularly embedded complete graph in a surface. In this paper, all automorphisms of complete maps of order n are determined by permutations on its vertices. Applying a scheme for enumerating maps on surfaces with a given underlying graph, the numbers of unrooted complete maps on orientable or non-orientable surfaces are obtained.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
