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In this paper, we first associate an Euclidean Jordan algebra <jats:italic>V<\/jats:italic> to <jats:italic>G<\/jats:italic> considering the real Euclidean Jordan algebra spanned by the identity of order n and the natural powers of <jats:italic>A.<\/jats:italic> Next, by the analysis of the spectra of an Hadamard logarithmic series of <jats:italic>V<\/jats:italic> we establish new admissibility conditions on the parameters of the strongly regular graph G.<\/jats:p>","DOI":"10.1088\/1742-6596\/1334\/1\/012020","type":"journal-article","created":{"date-parts":[[2019,10,18]],"date-time":"2019-10-18T09:14:15Z","timestamp":1571390055000},"page":"012020","update-policy":"https:\/\/doi.org\/10.1088\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Hadamard Logarithmic Series and Inequalities on The parameters of a Strongly Regular Graph"],"prefix":"10.1088","volume":"1334","author":[{"given":"Lu\u00eds A.","family":"Vieira","sequence":"first","affiliation":[]}],"member":"266","reference":[{"key":"JPCS_1334_1_012020bib1","doi-asserted-by":"crossref","first-page":"1148","DOI":"10.1016\/j.ejor.2004.11.027","article-title":"On the optimal parameter of a self-concordant barrier over a symmetric cone","volume":"169","author":"Cardoso","year":"2006","journal-title":"European Journal of Operational Research"},{"key":"JPCS_1334_1_012020bib2","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1016\/S0377-0427(97)00153-2","article-title":"Linear systems in Jordan algebras and primal-dual interior-point algorithms","volume":"86","author":"Faybusovich","year":"1997","journal-title":"Journal of Computational and Applied Mathematics"},{"key":"JPCS_1334_1_012020bib3","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1023\/A:1009701824047","article-title":"Euclidean Jordan Algebras and Interior-point Algorithms","volume":"1","author":"Faybusovich","year":"1997","journal-title":"Positivity"},{"key":"JPCS_1334_1_012020bib4","doi-asserted-by":"crossref","first-page":"29","DOI":"10.2307\/1968117","article-title":"On an algebraic generalization of the quantum mechanical formalism","volume":"35","author":"Jordan","year":"1934","journal-title":"Annals of Mathematics"},{"first-page":"800","year":"2018","author":"Vieira","key":"JPCS_1334_1_012020bib5"},{"key":"JPCS_1334_1_012020bib6","doi-asserted-by":"crossref","first-page":"881","DOI":"10.1023\/B:JOTH.0000013553.99598.cb","article-title":"Euclidean Jordan Algebras with strongly regular graphs","volume":"120","author":"Cardoso","year":"2004","journal-title":"Journal of Mathematical Sciences"},{"key":"JPCS_1334_1_012020bib7","first-page":"393","article-title":"On generalized binomial series and strongly regular graphs","volume":"4","author":"Mano","year":"2011","journal-title":"Proyecciones Journal of Mathematics"},{"key":"JPCS_1334_1_012020bib8","first-page":"1027","article-title":"Admissibility Conditions and Asymptotic Behaviour of Strongly Regular Graph","volume":"5","author":"Mano","year":"2011","journal-title":"International Journal of Mathematical Models and Methods in Applied Sciences"},{"key":"JPCS_1334_1_012020bib9","first-page":"256","article-title":"Alternating Schur Series and Necessary Conditions for the Existence of strongly Graphs","volume":"8","author":"Mano","year":"2014","journal-title":"International Journal of Mathematical Models and Methods in Applied Sciences Methods"},{"key":"JPCS_1334_1_012020bib10","doi-asserted-by":"crossref","first-page":"37","DOI":"10.4236\/am.2015.61005","article-title":"Generalized Krein parameters of a strongly regular graph","volume":"6","author":"Vieira","year":"2015","journal-title":"Applied Mathematics"},{"year":"2000","author":"Malley","key":"JPCS_1334_1_012020bib11"},{"key":"JPCS_1334_1_012020bib12","doi-asserted-by":"crossref","first-page":"1991","DOI":"10.1016\/j.laa.2008.11.015","article-title":"Some inertia theorems on Euclidean Jordan Algebras","volume":"430","author":"Gowda","year":"2009","journal-title":"Linear algebra and applications"},{"key":"JPCS_1334_1_012020bib13","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s10898-011-9734-x","article-title":"More results on Schur complements in Euclidean Jordan algebras","volume":"53","author":"Sznajder","year":"2012","journal-title":"Journal of Global Optimization"},{"first-page":"297","year":"2012","author":"Alizadeh","key":"JPCS_1334_1_012020bib14"},{"year":"1994","author":"Faraut","key":"JPCS_1334_1_012020bib15"},{"year":"1968","author":"Jacobson","key":"JPCS_1334_1_012020bib16"},{"year":"2000","author":"McCrimmon","key":"JPCS_1334_1_012020bib17"},{"year":"1993","author":"Godsil","key":"JPCS_1334_1_012020bib18"},{"key":"JPCS_1334_1_012020bib19","first-page":"A","article-title":"A condition on Higman\u2019s parameters","volume":"20","author":"Scott","year":"1973","journal-title":"Notices Amerc. 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