#cayley graph

[dreams-of-soft-rain]

[curiosamathematica]

Imagine a simple sliding puzzle with three pieces on the vertices of a tetrahedron, that you can slide around along the edges. There are 24 possible game states. All moves in the game are recorded in the depicted graph, known as the Nauru graph.

Larger sliding puzzles with more “holes” can have even more interesting graphs. You can find a couple of examples here. There is among others a quite innocent-looking puzzle with five pieces and one hole, resulting in a subdivision of the truncated cuboctahedron with a total of 120 vertices!

[weblingus]

http://mathworld.wolfram.com/CayleyGraph.html

[curiosamathematica]

Group theory meets graph theory: the sheets of the Cayley graph of the Baumslag-Solitar group BS(1,2) fit together into an infinite binary tree.

[themathkid]