Nodal Parity Invariants of Knotted Rigid Vertex Graphs

TL;DR

This paper introduces new invariants for rigid vertex graph embeddings using parity in Gauss codes, with applications to knot theory and protein folding topology.

Contribution

It presents novel non-local invariants based on parity, expanding tools for analyzing knotted graphs and their applications.

Findings

New invariants distinguish graph embeddings effectively.

Applicable to classical and virtual knot theory.

Potential use in understanding protein folding topology.

Abstract

This paper introduces new invariants of rigid vertex graph embeddings by using non-local combinatorial information that is available at each graphical node. The new non-local information that we use in this paper involves parity in the Gauss code of the underlying graph. We apply these methods to graphs in classical and virtual knot theory, and we give formulations for applications to the topology of protein folding.