REGULAR EMBEDDINGS OF A GRAPH

In this paper we study embeddings of a graph G in Euclidean space R" that are 'regular' in the following sense: given any two distinct vertices u and v of G, the distance between the corresponding points in R" equals a if u and v are adjacent, and equals β otherwise. It is shown that for any given value of s — (β2 — a2)/β29 the minimum dimension of a Euclidean space in which G is regularly embeddable is determined by the characteristic polynomials of G and (7.