Topological Symmetry Groups of Complete Bipartite Graphs

Topological Symmetry Groups of Complete Bipartite Graphs
复制标题

完全二分图的拓扑对称群

DOI：
--
复制
发表时间：
2014
期刊：
影响因子：
--
通讯作者：
Matt Pittluck
Matt Pittluck
中科院分区：
--
文献类型：
--
作者：
Kathleen Hake;B. Mellor;Matt Pittluck

文献摘要

被引文献

相似文献

复杂分子结构的对称性可以用嵌入图的{em拓扑对称群}来模拟。因此，理解哪些拓扑对称群可以通过特定的抽象图来实现是很重要的。这个问题已经在完全图中得到了回答;接下来考虑完全二部图是很自然的。在以前的工作中，我们对能实现同构于A_4 $，S_4 $或A_5 $的拓扑对称群的完全二部图进行了分类，本文确定了哪些完全二部图在S^3 $中有嵌入，其拓扑对称群同构于$mathbb{Z}_m$，$D_m$，$mathbb{Z}_r imes mathbb{Z}_s$或$（mathbb{Z}_r imes mathbb{Z}_s）ltimes mathbb{Z}_2$.
The symmetries of complex molecular structures can be modeled by the {em topological symmetry group} of the underlying embedded graph. It is therefore important to understand which topological symmetry groups can be realized by particular abstract graphs. This question has been answered for complete graphs; it is natural next to consider complete bipartite graphs. In previous work we classified the complete bipartite graphs that can realize topological symmetry groups isomorphic to $A_4$, $S_4$ or $A_5$; in this paper we determine which complete bipartite graphs have an embedding in $S^3$ whose topological symmetry group is isomorphic to $mathbb{Z}_m$, $D_m$, $mathbb{Z}_r imes mathbb{Z}_s$ or $(mathbb{Z}_r imes mathbb{Z}_s) ltimes mathbb{Z}_2$.