  We study the Erdos distance problem over finite Euclidean and non-Euclidean
spaces. Our main tools are graphs associated to finite Euclidean and
non-Euclidean spaces that are considered in Bannai-Shimabukuro-Tanaka (2004,
2007). These graphs are shown to be asymptotically Ramanujan graphs. The
advantage of using these graphs is twofold. First, we can derive new lower
bounds on the Erdos distance problems with explicit constants. Second, we can
construct many explicit tough Ramsey graphs R(3,k).
