Topological Symmetry Groups of the Generalized Petersen Graphs

Authors

Angelynn Álvarez, Embry–Riddle Aeronautical University
Erica Flapan, Pomona College
Mark Hunnell, Winston-Salem State University
John Hutchens, University of San Francisco
Emille Lawrence, University of San Francisco
Paul Lewis, Houston Christian University
Candice Price, Smith CollegeFollow
Ruth Vanderpool, University of Washington Tacoma

Document Type

Article

Publication Date

2025

Publication Title

Algebraic & Geometric Topology

Abstract

The topological symmetry group TSG(Γ) of an embedded graph Γ in S³ is the subgroup of the automorphism group of the graph which is induced by homeomorphisms of (S³,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 beTSG(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

Issue

25

First Page

4921

Last Page

4947

DOI

10.2140/agt.2025.25.4921

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Rights

© 2025 The Author(s)

Version

Version of Record

Recommended Citation

Álvarez, Angelynn; Flapan, Erica; Hunnell, Mark; Hutchens, John; Lawrence, Emille; Lewis, Paul; Price, Candice; and Vanderpool, Ruth, "Topological Symmetry Groups of the Generalized Petersen Graphs" (2025). Mathematics Sciences: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/mth_facpubs/204