Topological Symmetry Groups of Complete Graphs in the 3-sphere
نویسندگان
چکیده
The orientation preserving topological symmetry group of a graph embedded in the 3-sphere is the subgroup of the automorphism group of the graph consisting of those automorphisms which can be induced by an orientation preserving homeomorphism of the ambient space. We characterize all possible orientation preserving topological symmetry groups of embeddings of complete graphs in the 3-sphere.
منابع مشابه
Topological symmetry groups of graphs embedded in the 3-sphere
The topological symmetry group of a graph embedded in the 3-sphere is the group consisting of those automorphisms of the graph which are induced by some homeomorphism of the ambient space. We prove strong restrictions on the groups that can occur as the topological symmetry group of some embedded graph. In addition, we characterize the orientation preserving topological symmetry groups of embed...
متن کاملTopological Symmetry Groups of Graphs in 3-manifolds
We prove that for every closed, connected, orientable, irreducible 3-manifold there exists an alternating group An which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group G there is an embedding Γ of some graph in a hyperbolic rational homology 3-sphere such that the topological symmetry group of Γ is
متن کاملTopological Symmetry Groups of Small Complete Graphs
Topological symmetry groups were originally introduced to study the symmetries of non-rigid molecules, but have since been used to study the symmetries of any graph embedded in R. In this paper, we determine for each complete graph Kn with n ≤ 6, what groups can occur as topological symmetry groups or orientation preserving topological symmetry groups of some embedding of the graph in R.
متن کاملCLASSIFICATION OF TOPOLOGICAL SYMMETRY GROUPS OF Kn
In this paper we complete the classification of topological symmetry groups for complete graphs Kn by characterizing which Kn can have a cyclic group, a dihedral group, or a subgroup of Dm × Dm where m is odd, as its topological symmetry group.
متن کاملComplete Graphs whose Topological Symmetry Groups are Polyhedral
Characterizing the symmetries of a molecule is an important step in predicting its chemical behavior. Chemists have long used the group of rigid symmetries, known as the point group, as a means of representing the symmetries of a molecule. However, molecules which are flexible or partially flexible may have symmetries which are not included in the point group. Jon Simon [11] introduced the conc...
متن کامل