Abstract We consider the problem of realizing abstract graph symmetries by symmetries of the 3-sphere through spatial embeddings. The techniques usually used in preceding studies are based on the placement of vertices and edges, and the problem has been solved for several well-known families of graphs. This paper provides a technique which is applicable to any graph, and gives an affirmative answer to the problem for abstract graph symmetries given by finite subgroups of O ( 4 ) with some property on their singular sets.

中文翻译：

---

通过空间嵌入到 3 球体中实现图对称性

摘要 我们考虑通过空间嵌入通过 3 球体的对称性来实现抽象图对称性的问题。以往研究中通常使用的技术是基于顶点和边的放置，并且已经在几个著名的图族中解决了这个问题。本文提供了一种适用于任何图的技术，并给出了由 O ( 4 ) 的有限子群给出的抽象图对称性问题的肯定答案，这些子群在其奇异集上具有某些性质。