  Let $G$ be a graph on $n$ nodes. In this note, we prove that if $G$ is
$(r+1)$-vertex connected, $1 \leq r \leq n-2$, then there exists a
configuration $p$ in general position in $R^r$ such that the bar framework
$(G,p)$ is universally rigid. The proof is constructive and is based on a
theorem by Lovasz et al concerning orthogonal representations and connectivity
of graphs [12,13].
