Dispersed points and geometric embedding of complete bipartite graphs (Q807631)

Let X be a subset of \({\mathbb{R}}^ n\), the n-dimensional Euclidean space. The unit neighborhood graph has vertex set X and edge set all pairs of points at most one unit apart. The sphericity of G is the minimum n such that G is isomorphic to a unit neighborhood graph on some subset of \({\mathbb{R}}^ n\). The author gives upper and lower bounds on the sphericity of the complete bipartite graph \(K_{n,m}\). The exact values are given when \(m\leq 3\) and \(n\leq 10\).