Topological symmetry groups of the generalized Petersen graphs

Álvarez, Angelynn; Flapan, Erica; Hunnell, Mark; Hutchens, John; Lawrence, Emille; Lewis, Paul; Price, Candice; Vanderpool, Ruth

doi:10.2140/agt.2025.25.4921

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Topological symmetry groups of the generalized Petersen graphs

Angelynn Álvarez, Erica Flapan, Mark Hunnell, John Hutchens, Emille Lawrence, Paul Lewis, Candice Price and Ruth Vanderpool

Algebraic & Geometric Topology 25 (2025) 4921–4947

DOI: 10.2140/agt.2025.25.4921

Abstract

The topological symmetry group $TSG (Γ)$ of an embedded graph $Γ$ in $S^{3}$ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of $(S^{3}, Γ)$ . If we restrict to orientation-preserving homeomorphisms then we obtain the orientation-preserving topological symmetry group ${TSG}_{+} (Γ)$ . In this paper, we determine all groups that can be $TSG (Γ)$ or ${TSG}_{+} (Γ)$ for some embedding $Γ$ of a generalized Petersen graph other than the exceptional graphs $P (12, 5)$ and $P (24, 5)$ .

Keywords

topological symmetry groups, spatial graphs, symmetries, Petersen graph

Mathematical Subject Classification

Primary: 05C10, 57M15

Secondary: 92E10

References

Publication

Received: 3 April 2024

Revised: 15 July 2024

Accepted: 13 November 2024

Published: 20 November 2025

Authors

Angelynn Álvarez
Department of Mathematics Embry–Riddle Aeronautical University Prescott, AZ United States

Erica Flapan
Department of Mathematics and Statistics Pomona College Claremont, CA United States

Mark Hunnell
Department of Mathematics Winston-Salem State University Winston-Salem, NC United States

John Hutchens
Department of Mathematics and Statistics University of San Francisco San Francisco, CA United States

Emille Lawrence
Department of Mathematics and Statistics University of San Francisco San Francisco, CA United States

Paul Lewis
Department of Chemistry, Mathematics, and Physics Houston Christian University Houston, TX United States

Candice Price
Department of Mathematics and Statistics Smith College Northampton, MA United States

Ruth Vanderpool
School of Interdisciplinary Arts and Sciences University of Washington, Tacoma Tacoma, WA United States

Open Access made possible by participating institutions via Subscribe to Open.

Volume 25, issue 8 (2025)