RIGIDITY OF GRAPH SYMMETRIES IN THE 3-SPHERE

Abstract

In this paper we show that, for any 3-connected graph G, if an automorphism of G is realizable by a homeomorphism of (S3, G) then there is an embedding of G such that that automorphism is induced by a finite order homeomorphism of (S3, G). We then use this result to characterize which automorphisms of an arbitrary complete graph can be induced by a homeomorphism of S3 for some embedding of the graph.