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 Jordan algebra? with rank three spanned by In and the natural powe...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 Jordan algebra? with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of order n. Next we consider a basis? that is a Jordan frame of . Finally, by an algebraic asymptotic analysis of the second spectral decomposition of some Hadamard series associated to A we establish some inequalities over the spectra and over the parameters of a strongly regular graph.展开更多
文摘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 Jordan algebra? with rank three spanned by In and the natural powers of A that is a subalgebra of the Euclidean Jordan algebra of symmetric matrix of order n. Next we consider a basis? that is a Jordan frame of . Finally, by an algebraic asymptotic analysis of the second spectral decomposition of some Hadamard series associated to A we establish some inequalities over the spectra and over the parameters of a strongly regular graph.
