Topological Symmetry Groups of the Petersen Graph

TL;DR

This paper characterizes all possible topological symmetry groups of the Petersen graph embedded in three-dimensional space, providing a complete classification of symmetries based on the graph's embeddings.

Contribution

It offers a complete characterization of all groups realizable as topological symmetry groups of the Petersen graph in S^3, filling a gap in topological graph theory.

Findings

Identified all groups realizable as topological symmetry groups of the Petersen graph.

Provided explicit constructions for embeddings realizing each group.

Established constraints on possible symmetry groups for the Petersen graph.

Abstract

We characterize all groups which can occur as the topological symmetry group or the orientation preserving topological symmetry group of some embedding of the Petersen graph in S^3.