Nodal Parity Invariants of Knotted Rigid Vertex Graphs

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.