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%Vieira
%Luis","lvieira@fe.up.pt","
\section{Euclidean Jordan algebras and inequalities on the parameters and on the spectra  of a strongly  regular graph} By {\sl Luis Vieira}.    

\medskip \noindent Let $\tau$ be a strongly $(n,p;a,c)$ regular   graph, such that $0<c<p<n-1,$ $A$  his matrix of adjacency and let ${\cal V}_{n}$ be the Euclidean real space spanned by the powers of $A^j,j\in \mathbb{N}_{0}$  where the scalar product $\bullet|\bullet$ is defined by $x|y=\mbox{trace}(x \cdot y)$. In this work ones proves that ${\cal V}_{n}$ is an Euclidean Jordan algebra of rank 3 when one introduces in ${\cal V}_{n}$ the usual product of matrices.  Working inside the Euclidean Jordan algebra ${\cal V}_{n}$ with the the only complete system of orthogonal idempotents associated to A  one defines the generalized krein parameters of the  strongly $(n,p;a,c)$ regular graph $\tau.$ Finally one presents necessary conditions over the parameters and the spectra of the $\tau$ strongly $(n,p;a,c)$ regular graph.
%Euclidean Jordan Algebras, Graph theory","17","17C27","This work   can be classified also  05C50","06:51:35","Tue Mar 25 2008","193.136.33.216"
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