Spatial Graphs with Local Knots

Abstract

It is shown that for any locally knotted edge of a 3-connected graph in $S^3$, there is a ball that contains all of the local knots of that edge and is unique up to an isotopy setwise fixing the graph. This result is applied to the study of topological symmetry groups of graphs embedded in $S^3$.

20 pages, 3 figures; in v. 2 the proof of Theorem 1 has been clarified, and other minor revisions have been made

References in corpus (1)

• Topological Symmetry Groups of K_{4r+3}

Cited by in corpus (3)

• Enumeration and Identification of Unique 3D Spatial Topologies of Interconnected Engineering Systems Using Spatial Graphs
• Topological Symmetry Groups of the Petersen graphs
• Topological Symmetries of the Heawood family