Abstract:

The (orientation preserving) 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 orientation preserving diffeomorphism of the
ambient space. We show that not every finite group can occur as a topological
symmetry group of some embedded graph. Furthermore, we characterize which
groups can occur as topological symmetry groups of some embedded complete
graph.