  A d-dimensional framework is an embedding of the vertices and edges of a
graph in Euclidean space. A d-dimensional framework is globally rigid if every
other d-dimensional framework with the same edge lengths has the same pairwise
distances between the vertices. A graph is generically globally rigid in
dimension d (d-GGR) if every generic framework is globally rigid. The
d-dimensional framework of a d-GGR graph is universally rigid if for d' greater
than or equal to d every d'-dimensional framework with the same edge lengths
has the same pairwise distances between the vertices. We establish a strong
connection between global and universal rigidity by showing that all 1 and
2-GGR graphs and an infinite number of higher dimensional d-GGR graphs have a
generic universally rigid framework.
