Euclidean Jordan Algebras and Inequalities over the Spectrum of a Strongly Regular Graph

Abstract

Abstract Let G be a primitive strongly regular graph of order n with three distinct eigenvalues and A its adjacency matrix. In this paper we associate to A the 3—dimensional real Euclidean Jordan algebra A spanned by In and the natural powers of A equipped with the Jordan product of matrices and with inner product of two matrices being the trace of their Jordan product and next, by the spectral analysis of some elements of A we establish some inequalities over the spectrum and the parameters of a strongly regular graph.