Quotients of the Gordian and H(2)-Gordian graphs

  title={Quotients of the Gordian and H(2)-Gordian graphs},
  author={Christopher Flippen and Allison H. Moore and Essak Seddiq},
  journal={Journal of Knot Theory and Its Ramifications},
The Gordian graph and H(2)-Gordian graphs of knots are abstract graphs whose vertex sets represent isotopy classes of unoriented knots, and whose edge sets record whether pairs of knots are related by crossing changes or H(2)-moves, respectively. We investigate quotients of these graphs under equivalence relations defined by several knot invariants including the determinant, the span of the Jones polynomial, and an invariant related to tricolorability. We show, in all cases considered, that the… Expand

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