A graph is said to be flexible if the vertices of can be moved continuously so that (1) the distances between adjacent vertices are unchanged, and (2) at least two nonadjacent vertices change their mutual distances. A graph which is not flexible is said to be rigid.
Flexible Graph
See also
Rigid GraphExplore with Wolfram|Alpha
References
Maehara, H. "Distance Graphs in Euclidean Space." Ryukyu Math. J. 5, 33-51, 1992.Referenced on Wolfram|Alpha
Flexible GraphCite this as:
Weisstein, Eric W. "Flexible Graph." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/FlexibleGraph.html