Say that a graph $G$ is emph{representable in $R ^n$} if there is a map $f$ from its vertex set into the Euclidean space $R ^n$ such that $| f(x) - f(x)| = | f(y) - f(y)|$ iff ${x,x}$ and ${y, y}$ are both edges or both non-edges in $G$. The purpose of this note is to present the proof of the following result, due to Einhorn and Schoenberg: if $G$ finite is neither complete nor independent, then it is representable in $R ^{|G|-2}$. A similar result also holds in the case of finite complete edge-colored graphs.
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