Algebraic & Geometric Topology

Complete graphs whose topological symmetry groups are polyhedral

Erica Flapan, Blake Mellor, and Ramin Naimi

Full-text: Open access

Abstract

We determine for which m the complete graph Km has an embedding in S3 whose topological symmetry group is isomorphic to one of the polyhedral groups A4, A5 or S4.

Article information

Source
Algebr. Geom. Topol., Volume 11, Number 3 (2011), 1405-1433.

Dates
Received: 4 October 2010
Revised: 11 March 2011
Accepted: 19 March 2011
First available in Project Euclid: 19 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513715232

Digital Object Identifier
doi:10.2140/agt.2011.11.1405

Mathematical Reviews number (MathSciNet)
MR2821428

Zentralblatt MATH identifier
1270.57012

Subjects
Primary: 57M15: Relations with graph theory [See also 05Cxx] 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 05C10: Planar graphs; geometric and topological aspects of graph theory [See also 57M15, 57M25]

Keywords
topological symmetry group spatial graph

Citation

Flapan, Erica; Mellor, Blake; Naimi, Ramin. Complete graphs whose topological symmetry groups are polyhedral. Algebr. Geom. Topol. 11 (2011), no. 3, 1405--1433. doi:10.2140/agt.2011.11.1405. https://projecteuclid.org/euclid.agt/1513715232


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References

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