Euclidean Jordan Algebras and Some New Inequalities Over the Parameters of a Strongly Regular Graph

Abstract

Let’s consider a primitive strongly regular graph G and it’s adjacency matrix A. Next we consider the Euclidean subalgebra A of the Euclidean Jordan algebra of real symmetric matrices of order n, with the Jordan product and with the inner product of two matrices as being the usual trace of two matrices. Finally, we make a spectral analysis of an Hadamard series of an element of A to establish some new conditions over the spectrum and the parameters of the primitive strongly regular graph G.