Euclidean Distance Graph -- from Wolfram MathWorld

Let D be a set of positive numbers, then the D-Euclidean distance graph (or Euclidean distance-D graph) X(D) on a nonempty subset X of Euclidean space is the graph with vertex set X and edge set {(x,y):d(x,y) in D}, where d(x,y) is the Euclidean distance between vertices x and y. Maehara (1992) additionally require the set D to contain the distance 1. Examples include the Grabarchuk graph, which is the Euclidean distance-3 graph on the vertex set of the 4×4×4 grid graph, and the...