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 space spanned by the powers of $A$ over the reals where the scallar product $\bullet|\bullet$ is defined by $x|y={ trace}(x \cdot y).$ 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. In this Euclidean Jordan algebra one defines the modulus of a matrix, and afterwards one defines $|A|^x \forall x\in \mathbb{ R}.$ Working inside the Euclidean Jordan algebra ${ \cal V}_{ n}$ and making use of the properties of $|A|^x$ one defines the generalized krein parameters of the strongly $(n,p;a,c)$ regular graph $\tau$ and finally one presents necessary conditions over the parameters and the spectra of the $\tau$ strongly $(n,p;a,c)$ regular graph.
Categories: math.CO