Review Article

Euclidean Jordan algebras and some conditions over the spectra of a strongly regular graph

Department of Cívil Engineering of University of Porto, Street Roberto Frias, 0351-4200-465 Porto, Portugal

^* Corresponding author: lvieira@fe.up.pt

Received: 24 January 2019
Accepted: 13 May 2019

Abstract

Let G be a primitive strongly regular graph G such that the regularity is less than half of the order of G and A its matrix of adjacency, and let 𝒜 be the real Euclidean Jordan algebra of real symmetric matrices of order n spanned by the identity matrix of order n and the natural powers of A with the usual Jordan product of two symmetric matrices of order n and with the inner product of two matrices being the trace of their Jordan product. Next the spectra of two Hadamard series of 𝒜 associated to A² is analysed to establish some conditions over the spectra and over the parameters of G.