{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T15:44:11Z","timestamp":1717602251672},"reference-count":0,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2015,1,12]],"date-time":"2015-01-12T00:00:00Z","timestamp":1421020800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/3.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>The maximum multiplicity of an eigenvalue in a matrix whose graph is a tree, M<jats:sup>1<\/jats:sup>, was understood\nfully (froma combinatorial perspective) by C.R. Johnson, A. Leal-Duarte (Linear Algebra and Multilinear Algebra\n46 (1999) 139-144). Among the possible multiplicity lists for the eigenvalues of Hermitian matrices whose\ngraph is a tree, we focus upon M<jats:sup>2<\/jats:sup>, the maximum value of the sum of the two largest multiplicities when the\nlargest multiplicity is M<jats:sup>1<\/jats:sup>. Upper and lower bounds are given for M<jats:sup>2<\/jats:sup>. Using a combinatorial algorithm, cases\nof equality are computed for M<jats:sup>2<\/jats:sup>.<\/jats:p>","DOI":"10.1515\/spma-2015-0001","type":"journal-article","created":{"date-parts":[[2015,5,4]],"date-time":"2015-05-04T17:03:32Z","timestamp":1430759012000},"source":"Crossref","is-referenced-by-count":0,"title":["The maximum multiplicity and the two largest \nmultiplicities of eigenvalues in a Hermitian\nmatrix whose graph is a tree"],"prefix":"10.1515","volume":"3","author":[{"given":"Ros\u00e1rio","family":"Fernandes","sequence":"first","affiliation":[{"name":"Departamento de Matem\u00e1tica, Faculdade de Ci\u00eancias e Tecnologia, Universidade Nova de Lisboa, 2829-516 Caparica, Portugal"}]}],"member":"374","published-online":{"date-parts":[[2015,1,12]]},"container-title":["Special Matrices"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2015-0001\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2015-0001\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T14:40:55Z","timestamp":1717598455000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2015-0001\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,5,7]]}},"alternative-id":["10.1515\/spma-2015-0001"],"URL":"https:\/\/doi.org\/10.1515\/spma-2015-0001","relation":{},"ISSN":["2300-7451"],"issn-type":[{"value":"2300-7451","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,1,12]]}}}