Complete graphs whose topological symmetry groups are polyhedral

Erica Flapan; Blake Mellor; Ramin Naimi

doi:10.2140/agt.2011.11.1405

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Home > Journals > Algebr. Geom. Topol. > Volume 11 > Issue 3 > Article

2011 Complete graphs whose topological symmetry groups are polyhedral

Erica Flapan, Blake Mellor, Ramin Naimi

Algebr. Geom. Topol. 11(3): 1405-1433 (2011). DOI: 10.2140/agt.2011.11.1405

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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 $S_{4}$ .

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Erica Flapan. Blake Mellor. Ramin Naimi. "Complete graphs whose topological symmetry groups are polyhedral." Algebr. Geom. Topol. 11 (3) 1405 - 1433, 2011. https://doi.org/10.2140/agt.2011.11.1405

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Received: 4 October 2010; Revised: 11 March 2011; Accepted: 19 March 2011; Published: 2011

First available in Project Euclid: 19 December 2017

zbMATH: 1270.57012

MathSciNet: MR2821428

Digital Object Identifier: 10.2140/agt.2011.11.1405

Subjects:

Primary: 57M15 , 57M25

Secondary: 05C10

Keywords: spatial graph , topological symmetry group

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Erica Flapan, Blake Mellor, Ramin Naimi "Complete graphs whose topological symmetry groups are polyhedral," Algebraic & Geometric Topology, Algebr. Geom. Topol. 11(3), 1405-1433, (2011)

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