The project has as aim to study Neumaier and Deza graphs by means of geometric methods and techniques from spectral graph theory. Both Neumaier graphs and Deza graphs are generalizations of so-called strongly regular graphs, while still possessing a high degree of structure and regularity. They are related to many other interesting and well-studied families of graphs such as Cayley graphs, walk-regular graphs and Q-polynomial distance-regular graphs.

We aim at finding new geometric and algebraic constructions of these graphs, and to prove the nonexistence of certain of these graphs. Special attention will go to the case where the graph has exactly five eigenvalues, as the existence problem for such Neumaier graphs is still open.

Neumaier graphs with exactly one value for the mu-parameter (the strongly regular graphs) have already been characterized in several ways, and the intenton is to find similar characterizations in the case that there are two possible values for this parameter.