The label bracket for knotted trivalent graphs

TL;DR

This paper introduces a new label bracket invariant for knotted trivalent graphs in three-dimensional space, extending previous work to provide a tool for distinguishing such graphs up to isotopy.

Contribution

It generalizes the label bracket construction to knotted trivalent graphs, establishing it as an isotopy invariant.

Findings

The label bracket is an isotopy invariant for knotted trivalent graphs.

The construction extends previous invariants to a broader class of graphs.

Provides a new method for classifying knotted graphs in 3D space.

Abstract

We generalize the construction of Akimova and Manturov, define the label bracket for knotted trivalent graphs in $\mathbb{R}^3$ and show it defines an isotopy invariant of such graphs.