Explorations on Conjugations of Local Rotations

Abstract

The process of manipulating single local rotations of vertices can represent standard topological graph theory techniques to add vertices or edges to an existing embedding. This paper looks to find patterns of these local rotations we can generalize. We start by reviewing the local rotations of vertices of small degree (3, 4, and 5). At those local rotations, we propose some hypotheses to be tested on local rotations of higher degree. We then move to outline an algorithm that can be used to analyze vertices of larger degrees programmatically.