Complete graphs whose topological symmetry groups are polyhedral

Flapan, Erica; Mellor, Blake; Naimi, Ramin

doi:10.2140/agt.2011.11.1405

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Complete graphs whose topological symmetry groups are polyhedral

Erica Flapan, Blake Mellor and Ramin Naimi

Algebraic & Geometric Topology 11 (2011) 1405–1433

DOI: 10.2140/agt.2011.11.1405

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 $S_{4}$ .

Keywords

topological symmetry group, spatial graph

Mathematical Subject Classification 2010

Primary: 57M15, 57M25

Secondary: 05C10

References

Publication

Received: 4 October 2010

Revised: 11 March 2011

Accepted: 19 March 2011

Published: 17 May 2011

Authors

Erica Flapan
Department of Mathematics Pomona College 610 N College Ave Claremont CA 91711 USA

Blake Mellor
Department of Mathematics Loyola Marymount University 1 LMU Drive University Hall, Suite 2700 Los Angeles CA 90045 USA

Ramin Naimi
Department of Mathematics Occidental College Los Angeles CA 90041 USA

Volume 11, issue 3 (2011)