On Some Applications of Graph Theory to Geometry

Abstract

Let [Pn(k)] be the class of all subsets Pn(k) of the k-dimensional Euclidean space consisting of n distinct points and having diameter 1. Denote by dk(n, r) the maximum number of times a given distance r can occur among points of a set Pn(k).PutIn other words Dk(n) denotes the maximum number of times the same distance can occur between n suitably chosen points in k-dimensional space.