Symmetries of embedded complete bipartite graphs

TL;DR

This paper characterizes which automorphisms of complete bipartite graphs can be realized by homeomorphisms of their embeddings in three-dimensional space, contributing to the understanding of symmetries in spatial graph embeddings.

Contribution

It provides a characterization of automorphisms of $K_{n,m}$ induced by homeomorphisms in embeddings in $S^3$, advancing the study of symmetries in spatial graph theory.

Findings

Identifies automorphisms realizable by homeomorphisms in embeddings

Provides criteria for automorphism realizability in $K_{n,m}$

Enhances understanding of symmetries in spatial graph embeddings

Abstract

We characterize which automorphisms of an arbitrary complete bipartite graph $K_{n,m}$ can be induced by a homeomorphism of some embedding of the graph in $S^3$.