Graphs of integral distance and their properties

Abstract

Understanding the geometries of points in space has been attractive to mathematicians for ages. As a model, twelve years ago, Kurz and Meyer [32] considered point sets in the m-dimensional a ne space Fmq over a nite eld Fq with q = pr elements, p prime, where each squared Euclidean distance of two points is a square in Fq: The latter points are said to be at integral distance in Fmq , and the sets above are called integral point sets.