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Binomial Hadamard Series and Inequalities over the Spectra of a Strongly Regular Graph
Department of Civil Engineering, University of Porto, Porto, Portugal
- 1 Department of Civil Engineering, University of Porto, Porto, Portugal
Applied Mathematics·Volume 09 (2018)·Pages 1055–1071·Published 17 September 2018·DOI10.4236/am.2018.99071
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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 Jordan algebra with rank three spanned by I n 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.
KeywordsEuclidean Jordan AlgebrasGraph TheoryStrongly Regular Graphs
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