Some Results on the Spectra of Strongly Regular Graphs

Let G be a strongly regular graph whose adjacency matrix is A. We associate a real finite dimensional Euclidean Jordan algebra V, of rank three to the strongly regular graph G, spanned by I and the natural powers of A, endowed with the Jordan product of matrices and with the inner product as being the usual trace of matrices. Finally, by the analysis of the binomial Hadamard series of an element of V, we establish some inequalities on the parameters and on the spectrum of a strongly regular graph like those established in theorems 3 and 4.