Strongly Regular Graphs and Euclidean Jordan Algebras

In this book we do a survey of the problem of finding suitable admissibility conditions on the parameters of strongly regular graphs and add our own contribution to the area. The matrix space spanned by the identity matrix and the adjacency matrix of a strongly regular graph is an Euclidean Jordan algebra with rank three. In this environment the Krein parameters of a strongly regular graph are generalized and some conditions on the parameters of a strongly regular graph are deduced. The results obtained were directly applied to the Krein parameters of the more general structures given by symmetric association schemes with any number of classes.