Algebraic & Geometric Topology

Complete graphs whose topological symmetry groups are polyhedral

Erica Flapan, Blake Mellor, and Ramin Naimi

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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]

topological symmetry group spatial graph


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.

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