Classification of (uncolored) bonded knots and links

Boštjan Gabrovšek; Matic Simonič; Wanda Niemyska

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arXiv · 2603.18768

Classification of (uncolored) bonded knots and links

Boštjan Gabrovšek·Matic Simonič·Wanda Niemyska

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Abstract

We present a systematic classification of uncolored bonded knots with singularity number at most seven. Bonded knots provide a topological model for closed protein chains with intramolecular bridges, such as disulfide bonds. Following the tradition of knot tabulation, we describe a procedure based on the generation of planar graphs, their conversion into bonded knot diagrams, and the use of the Yamada polynomial together with brute-force Reidemeister moves to distinguish topological knotted types.

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Boštjan Gabrovšek, Matic Simonič, Wanda Niemyska. 2026-03-19. Classification of (uncolored) bonded knots and links. https://arxiv.org/abs/2603.18768

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