Rigidity of Graph Symmetries in the 3-Sphere
Embedded graphs, symmetries of graphs, chirality
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.
© 1995 World Scientific Publishing Co.
E. Flapan, Rigidity of Graph Symmetries in the 3-Sphere, Journal of Knot Theory and its Ramifications, 4 (1995) 373-388. doi: 10.1142/S0218216595000181