I would like to ask on the number of different drawings of the unit distance representation of a graph, found through a semidefinite program (see www.cs.elte.hu/~lovasz/semidef.ps , p. 20-22). Since we find the Gram matrix, there should be not just one unique unit distance representation having the SAME dimension and SAME radius of course (after analyzing the Gram matrix in vectors, since one Gram matrix may give many pairs of matrices multiplied together).
So, do we have any information on a bound of the possible different drawings of a graph obtained by this SDP? Is it polynomial for example? Thanks