Given $N$ points $\{x_i\}$ in 3D space, and their pairwise distances $\{r_{ij}\}$, does anyone know what is the minimum number of pairwise distances are required to make the graph "fixed" and how do we find such pairs?
I know that if three points are not in the same straight line, the distances to these three points would uniquely determine the location of another point. But if they are in the same line, that would not be the case. I wonder if there exists some general results for all possible cases for this problem? Thank you!
