  A simple graph G is said to be representable in a real vector space of
dimension m if there is an embedding of the vertex set in the vector space such
that the Euclidean distance between any two distinct vertices is one of only
two distinct values a or b, with distance a if the vertices are adjacent and
distance b otherwise. The Euclidean representation number of G is the smallest
dimension in which G is representable. In this note, we bound the Euclidean
representation number of a graph using multiplicities of the eigenvalues of the
adjacency matrix. We also give an exact formula for the Euclidean
representation number using the main angles of the graph.
