We describe two locally finite graphs naturally associated to each knot type , called Reidemeister graphs. We determine several local and global properties of these graphs and prove that in one case the graph-isomorphism type is a complete knot invariant up to mirroring. Lastly, we introduce another object, relating the Reidemeister and Gordian graphs, and determine some of its properties.
"The Reidemeister graph is a complete knot invariant." Algebr. Geom. Topol. 20 (2) 643 - 698, 2020. https://doi.org/10.2140/agt.2020.20.643