An Extension of the sl(n) Polynomial to Knotted 4-Valent Graphs - Caprau , Carmen; Wiest, Victoria (The PUMP Journal of Undergraduate Research, 2026)
We use planar 4-valent graphs and a graphical calculus involving such graphs to construct an invariant for balanced-oriented, knotted 4-valent graphs. Our invariant is an extension of the sl(n) polynomial for classical knots and links. We also provide a minimal generating set of Reidemeister-type moves for diagrams of balanced-oriented, knotted 4-valent graphs.