Complete graphs whose topological symmetry groups are polyhedral

Abstract

We determine for which $m$, the complete graph $K_m$ has an embedding in $S^3$ whose topological symmetry group is isomorphic to one of the polyhedral groups: $A_4$, $A_5$, or $S_4$.

27 pages, 12 figures; v.2 and v.3 include minor revisions

References in corpus (1)

• Complete graphs whose topological symmetry groups are polyhedral

Cited by in corpus (9)

• Complete graphs whose topological symmetry groups are polyhedral
• Classification of topological symmetry groups of $K_n$
• Topological Symmetry Groups for Small Complete Graphs
• Topological Symmetries of the Heawood family
• Intrinsic Chirality of Multipartite Graphs
• Complete bipartite graphs whose topological symmetry groups are polyhedral
• Topological Symmetry Groups of Möbius Ladders
• Topological Symmetry Groups of the Petersen Graph
• Topological Symmetry Groups of the Heawood Graph