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

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