Conference graph

In the mathematical area of graph theory, a conference graph is a strongly regular graph with parameters "v", and It is the graph associated with a symmetric conference matrix, and consequently its order "v" must be 1 (modulo 4) and a sum of two squares.
Conference graphs are known to exist for all small values of "v" allowed by the restrictions, e.g., "v" = 5, 9, 13, 17, 25, 29, and (the Paley graphs) for all prime powers congruent to 1 (modulo 4). However, there are many values of "v" that are allowed, for which the existence of a conference graph is unknown.
The eigenvalues of a conference graph need not be integers, unlike those of other strongly regular graphs. If the graph is connected, the eigenvalues are "k" with multiplicity 1, and two other eigenvalues, 
each with multiplicity 
References.
Brouwer, A.E., Cohen, A.M., and Neumaier, A. (1989), Distance Regular Graphs. Berlin, New York: Springer-Verlag. , 