A uniqueness theorem for Delaunay graphs (Q359369)

A graph is called a Delauney graph if its edges are segments whose orthogonal hyperplanes through their midpoints form the faces of a Voronoi domain. The author proves a necessary and sufficient condition for two isomoprphic Delauney graphs to be congruent. The proof uses an inductive argument on the congruence of isomorphic pairs of Delauney polyhedra of the two isomorphic Delauney graphs.