# Tagged Questions

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### Link diagrams and Reidemeister moves

I am studying Knots on "Algebraic Graph Theory" written by Godsil & Royle. They state the following theorem: $\underline{Theorem}$ Two link diagrams determine the same link if and only if one can ...
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### How do you specify a link to a blind combinatorialist?

Regular projections of links look like graphs in the plane. So I'm wondering if it would be possible to specify a link up to isotopy with purely combinatorial data about this graph. If so, what kind ...
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### Determine the multiplicity of knots for a graph

Here are my two questions: Given a finite connected non-oriented planar graph, is there a way to determine whether or not it is possible to derive a single non-trivial knot diagram from this graph, ...
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### Medial graph and Seifert surface

To generate a medial graph from a knot one has to shade the knot diagram in the checkerboard pattern first. The infinite region is always black. Let us call this a surface. I would like to know ...
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### Uniqueness of Seifert graphs

If we make the bands and disks of a Seifert surface really small and really thin the surface collapses to a graph. It is called a Seifert graph. If it is not a directed and weighted graph, can we ...
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### Hamiltonian of one and two unknots

Recently I calculated the Ising Hamiltonian of a Hopf link. First, I colored the Hopf link in a checker board pattern and drew the Seifert surface from it. Considering the shaded regions as vertices ...
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### Knots and graphs

Every knot gives rise to a number of 4-regular planar graphs - by regular projections onto the plane - which just have to be enriched by an over/under flag for every vertex to be able to reconstruct ...