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      Euclidean Jordan algebras and some conditions over the spectra of a strongly regular graph

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          Abstract

          Let G be a primitive strongly regular graph G such that the regularity is less than half of the order of G and A its matrix of adjacency, and let 𝒜 be the real Euclidean Jordan algebra of real symmetric matrices of order n spanned by the identity matrix of order n and the natural powers of A with the usual Jordan product of two symmetric matrices of order n and with the inner product of two matrices being the trace of their Jordan product. Next the spectra of two Hadamard series of 𝒜 associated to A 2 is analysed to establish some conditions over the spectra and over the parameters of G.

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          Most cited references 26

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          Second-order cone programming

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            Strongly regular graphs, partial geometries and partially balanced designs

             Raj Bose (1963)
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              Linear systems in Jordan algebras and primal-dual interior-point algorithms

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                Author and article information

                Affiliations
                [1 ] Department of Cívil Engineering of University of Porto, , Street Roberto Frias, 0351-4200-465 Porto, Portugal,
                Author notes
                [* ]Corresponding author: lvieira@ 123456fe.up.pt
                Journal
                fopen
                https://www.4open-sciences.org
                4open
                4open
                EDP Sciences
                2557-0250
                02 July 2019
                02 July 2019
                2019
                : 2
                : ( publisher-idID: fopen/2019/01 )
                10.1051/fopen/2019017 fopen190010
                © L. Vieira, Published by EDP Sciences, 2019

                This is an Open Access article distributed under the terms of the Creative Commons Attribution License ( http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

                Counts
                Figures: 3, Tables: 2, Equations: 502, References: 38, Pages: 19
                Product
                Self URI (journal page): https://www.4open-sciences.org/
                Categories
                Mathematics - Applied Mathematics
                Review Article
                Mathematical Models
                Custom metadata
                4open 2019, 2, 21
                2019
                2019
                2019

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