Applications of numbered undirected graphs

Numbered undirected graphs are becoming an increasingly useful family of mathematical models for a broad range of applications. They have found usage in various coding theory problems, including the design of good radar-type codes, synch-set codes and convolutional codes with optimal autocorrelation properties. They facilitate the optimal nonstandard encodings of integers. They have also been applied to determining ambiguities in X-ray crystallographic analysis, to design of a communication network addressing system, to determination of optimal circuit layouts, and to problems in additive number theory. An attempt has been made to systematically present all of these diverse applications in a unifying framework and to indicate the existence of additional applications and to suggest directions for additional research.