一类弧正则多面体的同构判别准则
A criterion for isomorphism of a class of arc-regular polyhedra
任凯慧 1袁凯 1王燕1
作者信息
- 1. 烟台大学数学与信息科学学院，烟台 264000
- 折叠
摘要
连通图在连通闭曲面上的2-胞腔嵌入, 称为地图. 多面体是一类具有钻石特性的地图. 如果多面体的自同构群中存在一个点稳定子群为二面体群的子群~$G$, 使得群~$G$ 在多面体的弧集合上作用正则, 并在其面集合上恰有两个轨道, 那么此多面体称为~$2_{0,1}$ 型多面体. 本文给出了~$2_{0,1}$ 型多面体互不同构的充分必要条件.
Abstract
A 2-cell embedding of a connected graph into a connected closed surface is called a map. A polyhedron is a type of map with diamond properties. If the automorphism group of a polyhedron contains a subgroup $G$ with a vertex stabilizer--- a dihedral group, such that $G$ acts regularly on the set of arcs of the polyhedron and has exactly two orbits on its set of faces, then this polyhedron is called a polyhedron of type $2_{0,1}$. In this paper, we give a necessary and sufficient condition for two polyhedra of type $2_{0,1}$ to be non-isomorphic.关键词
基础数学/多面体/弧正则Key words
Foundation of Mathematics/Polyhedra/Arc-regular引用本文复制引用
任凯慧,袁凯,王燕.一类弧正则多面体的同构判别准则[EB/OL].(2026-04-07)[2026-04-08].http://www.paper.edu.cn/releasepaper/content/202604-56.学科分类
数学
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