This website presents animations of various movable graphs.
The motions are either known, like Dixon’s constructions for bipartite graphs, or they come from constructions described in our papers Graphs with Flexible Labelings and Graphs with Flexible Labelings allowing Injective Realizations. The notation of graphs comes from the latter paper. Actually, the presented animations cover all graphs up to 8 vertices satisfying the necessary condition of movability, namely, the constant distance closure is not a complete graph. In other words, they show that up to 8 vertices, the necessary condition is also sufficient (which is not the case in general).
Please, choose group of graphs from the menu.
Animations are created using SVG. Animated SVG is supported by Chrome and Firefox. In case that the animations do not work in your browser, you can download them in GIF format.
For some graphs, a collision-free linkage following the motion is provided. These models come from discussions with Jiayue Qi.