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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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