Rubik's graph is the Cayley graph of Rubik's group. The graph diameter of this graph is sometimes known as God's number, and was shown in Aug. 2010 to be equal to 20 (Rokicki et al. 2010).
Rubik's Graph
See also
Cayley Graph, God's Number, Rubik's Cube, Rubik's GroupExplore with Wolfram|Alpha
References
Rokicki, T.; Kociemba, H.; Davidson, M.; and Dethridge, J. "God's Number is 20." http://www.cube20.org/.Referenced on Wolfram|Alpha
Rubik's GraphCite this as:
Weisstein, Eric W. "Rubik's Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RubiksGraph.html