Topological symmetry groups of small complete graphs (Q2412295)

Summary: 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 \(\mathbb R^3\). In this paper, we determine for each complete graph \(K_n\) with \(n\leq 6\), what groups can occur as topological symmetry groups or orientation preserving topological symmetry groups of some embedding of the graph in \(\mathbb R^3\).