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Binomial Hadamard Series and Inequalities over the Spectra of a Strongly Regular Graph

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Document pages: 17 pages

Abstract: Let G be a primitive strongly regular graph of order n and A is adjacency matrix.In this paper we first associate to A a real 3-dimensional Euclidean Jordanalgebra  with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix oforder n. Next we consider a basis  that is a Jordan frame of . Finally,by an algebraic asymptotic analysis of the second spectral decomposition ofsome Hadamard series associated to A we establish some inequalities over thespectra and over the parameters of a strongly regular graph.

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