{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:37:41Z","timestamp":1760150261630,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T00:00:00Z","timestamp":1698624000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CMUP","award":["UID\/MAT\/00144\/2019","PT2020"],"award-info":[{"award-number":["UID\/MAT\/00144\/2019","PT2020"]}]},{"name":"FCTwith national (MCTES) and European structural funds through the programs FEDER","award":["UID\/MAT\/00144\/2019","PT2020"],"award-info":[{"award-number":["UID\/MAT\/00144\/2019","PT2020"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, in the environment of Euclidean Jordan algebras, we establish some inequalities over the Krein parameters of a symmetric association scheme and of a strongly regular graph. Next, we define the modified Krein parameters of a strongly regular graph and establish some admissibility conditions over these parameters. Finally, we introduce some relations over the Krein parameters of a strongly regular graph.<\/jats:p>","DOI":"10.3390\/sym15111997","type":"journal-article","created":{"date-parts":[[2023,10,30]],"date-time":"2023-10-30T12:50:42Z","timestamp":1698670242000},"page":"1997","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Euclidean Jordan Algebras, Symmetric Association Schemes, Strongly Regular Graphs, and Modified Krein Parameters of a Strongly Regular Graph"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1174-0082","authenticated-orcid":false,"given":"Lu\u00eds Almeida","family":"Vieira","sequence":"first","affiliation":[{"name":"Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Vieira, L.A. (2022, January 20). An Euclidean Jordan algebra of symmetric matrices closed for the Schur product of matrices. Proceedings of the 27th International Conference on Circuits, Systems, Communications and Computers (CSCC), Rhodes Island, Greece.","DOI":"10.1109\/CSCC58962.2023.00044"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Faraut, J., and Kor\u00e1nyi, A. (1994). Analysis on Symmetric Cones, Oxford Science Publications.","DOI":"10.1093\/oso\/9780198534778.001.0001"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Bailey, R.A. (2004). Association Schemes: Designed Experiments, Algebra and Combinatorics, Cambridge University Press. Cambridge Studies in Advanced Mathematics.","DOI":"10.1017\/CBO9780511610882"},{"key":"ref_4","unstructured":"Zieschang, P.H. (2005). Theory of Association Schemes, Springer. 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Optim."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1119","DOI":"10.1007\/s11590-021-01793-2","article-title":"Commutation principles for optimization problems on spectral sets in Euclidean Jordan algebras","volume":"16","author":"Gowda","year":"2022","journal-title":"Optim. Lett."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1016\/j.laa.2023.03.011","article-title":"A Fiedler-type determinantal inequality in Euclidean Jordan algebras","volume":"667","author":"Sossa","year":"2023","journal-title":"Linear Algebra Its Appl."},{"key":"ref_10","first-page":"21","article-title":"Euclidean Jordan algebras and some conditions over the spectra of a strongly regular graph","volume":"2","author":"Vieira","year":"2019","journal-title":"4 Open"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"156","DOI":"10.13001\/ela.2021.5585","article-title":"An analog of Thompson\u2019s triangle inequality in Euclidean Jordan algebras","volume":"37","author":"Tao","year":"2021","journal-title":"Electron. J. Linear Algebra"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1007\/s11117-010-0086-4","article-title":"Some inequalities involving determinants, eigenvalues, and Schur complements in Euclidean Jordan algebras","volume":"15","author":"Gowda","year":"2011","journal-title":"Positivity"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"389","DOI":"10.2140\/pjm.1963.13.389","article-title":"Strongly regular graphs, partial geometries, and partially balanced designs","volume":"13","author":"Bose","year":"1963","journal-title":"Pac. J. Math"},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Godsil, C., and Royle, G.F. (2001). Algebraic Graph Theory, Springer.","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"ref_15","first-page":"A-97","article-title":"A condition on Higman\u2019s parameters","volume":"20","author":"Scott","year":"1973","journal-title":"Not. Am. Math. 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Rep"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/1997\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:14:17Z","timestamp":1760130857000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/11\/1997"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,10,30]]},"references-count":16,"journal-issue":{"issue":"11","published-online":{"date-parts":[[2023,11]]}},"alternative-id":["sym15111997"],"URL":"https:\/\/doi.org\/10.3390\/sym15111997","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2023,10,30]]}}}