Topological Symmetry Groups of K_{4r+3}

TL;DR

This paper introduces the concept of topological symmetry groups to analyze symmetries in non-rigid molecules and characterizes all possible groups for embeddings of K_{4r+3} in three-dimensional space.

Contribution

It defines topological symmetry groups and completely characterizes their possible groups for embeddings of K_{4r+3} in S^3.

Findings

Characterization of all topological symmetry groups for K_{4r+3} embeddings

Introduction of topological symmetry groups for molecular symmetry analysis

Complete classification of symmetry groups for specific complete graphs

Abstract

We present the concept of the topological symmetry group as a way to analyze the symmetries of non-rigid molecules. Then we characterize all of the groups which can occur as the topological symmetry group of an embedding of the complete graph K_{4r+3} in S^3.