{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T17:53:14Z","timestamp":1732038794665},"reference-count":11,"publisher":"Walter de Gruyter GmbH","issue":"1","license":[{"start":{"date-parts":[[2019,1,1]],"date-time":"2019-01-01T00:00:00Z","timestamp":1546300800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,1,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>We consider a particular class of signed threshold graphs and their eigenvalues. If <jats:italic>\u0120<\/jats:italic> is such a threshold graph and <jats:italic>Q<\/jats:italic>(<jats:italic>\u0120<\/jats:italic> ) is a quotient matrix that arises from the equitable partition of <jats:italic>\u0120<\/jats:italic> , then we use a sequence of elementary matrix operations to prove that the matrix <jats:italic>Q<\/jats:italic>(<jats:italic>\u0120<\/jats:italic> ) \u2013 <jats:italic>xI<\/jats:italic> (<jats:italic>x<\/jats:italic> \u2208 \u211d) is row equivalent to a tridiagonal matrix whose determinant is, under certain conditions, of the constant sign. In this way we determine certain intervals in which <jats:italic>\u0120<\/jats:italic> has no eigenvalues.<\/jats:p>","DOI":"10.1515\/spma-2019-0014","type":"journal-article","created":{"date-parts":[[2019,12,14]],"date-time":"2019-12-14T18:08:26Z","timestamp":1576346906000},"page":"218-225","source":"Crossref","is-referenced-by-count":4,"title":["A note on the eigenvalue free intervals of some classes of signed threshold graphs"],"prefix":"10.1515","volume":"7","author":[{"given":"Milica","family":"An\u0111eli\u0107","sequence":"first","affiliation":[{"name":"Department of Mathematics , Kuwait University , Safat 13060, Kuwait"}]},{"given":"Tamara","family":"Koledin","sequence":"additional","affiliation":[{"name":"Faculty of Electrical Engineering , University of Belgrade , Bulevar kralja Aleksandra 73, Belgrade , Serbia"}]},{"given":"Zoran","family":"Stani\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics , University of Belgrade , Studentski trg 16, Belgrade , Serbia"}]}],"member":"374","published-online":{"date-parts":[[2019,12,2]]},"reference":[{"key":"2021102520013772094_j_spma-2019-0014_ref_001_w2aab3b7c28b1b6b1ab1ab1Aa","doi-asserted-by":"crossref","unstructured":"[1] C.O. Aguilar, J. Lee, E. Piato, B.J. Schweitzer, Spectral characterizations of anti-regular graphs, Linear Algebra Appl., 557 (2018), 84-104.","DOI":"10.1016\/j.laa.2018.07.028"},{"key":"2021102520013772094_j_spma-2019-0014_ref_002_w2aab3b7c28b1b6b1ab1ab2Aa","unstructured":"[2] A. Alazemi, M. An\u0111eli\u0107, T. Koledin, Z. K. Stani\u0107, Eigenvalue-free intervals of distance matrices of threshold and chain graphs, Linear Multilinear Algebra, submitted."},{"key":"2021102520013772094_j_spma-2019-0014_ref_003_w2aab3b7c28b1b6b1ab1ab3Aa","doi-asserted-by":"crossref","unstructured":"[3] A.E. Brouwer, W.H. Haemers, Spectra of graphs, Springer, 2011.","DOI":"10.1007\/978-1-4614-1939-6"},{"key":"2021102520013772094_j_spma-2019-0014_ref_004_w2aab3b7c28b1b6b1ab1ab4Aa","doi-asserted-by":"crossref","unstructured":"[4] M. An\u0111eli\u0107, C. M. da Fonseca, Sufficient conditions for positive definiteness of tridiagonal matrices revisited, Positivity, 15 (2011), 155\u2013159.","DOI":"10.1007\/s11117-010-0047-y"},{"key":"2021102520013772094_j_spma-2019-0014_ref_005_w2aab3b7c28b1b6b1ab1ab5Aa","doi-asserted-by":"crossref","unstructured":"[5] D. Cvetkovi\u0107, P. Rowlinson, S.K. Simi\u0107, An Introduction to the Theory of Graph Spectra, Cambridge University Press, Cambridge, 2010.","DOI":"10.1017\/CBO9780511801518"},{"key":"2021102520013772094_j_spma-2019-0014_ref_006_w2aab3b7c28b1b6b1ab1ab6Aa","doi-asserted-by":"crossref","unstructured":"[6] E. Ghorbani, Eigenvalue-free interval for threshold graphs, Linear Algebra Appl., 583 (2019), 300-305.","DOI":"10.1016\/j.laa.2019.08.028"},{"key":"2021102520013772094_j_spma-2019-0014_ref_007_w2aab3b7c28b1b6b1ab1ab7Aa","doi-asserted-by":"crossref","unstructured":"[7] D.P. Jacobs, V. Trevisan, and F. Tura, Eigenvalue location in threshold graphs, Linear Algebra Appl., 439 (2013), 2762-2773.","DOI":"10.1016\/j.laa.2013.07.030"},{"key":"2021102520013772094_j_spma-2019-0014_ref_008_w2aab3b7c28b1b6b1ab1ab8Aa","doi-asserted-by":"crossref","unstructured":"[8] D.P. Jacobs, V. Trevisan, F. Tura, Eigenvalues and energy in threshold graphs, Linear Algebra Appl., 465 (2015), 412\u2013425.","DOI":"10.1016\/j.laa.2014.09.043"},{"key":"2021102520013772094_j_spma-2019-0014_ref_009_w2aab3b7c28b1b6b1ab1ab9Aa","doi-asserted-by":"crossref","unstructured":"[9] C.R. Johnson, M. Neumann, M.J. Tsatsomeros, Conditions for the positivity of determinants, Linear Multilinear Algebra, 40 (1996), 241\u2013248.","DOI":"10.1080\/03081089608818442"},{"key":"2021102520013772094_j_spma-2019-0014_ref_010_w2aab3b7c28b1b6b1ab1ac10Aa","unstructured":"[10] V.R. Mahadev, U.N. Peled, Threshold Graphs and Related Topics, North-Holland, Amsterdam, 1995."},{"key":"2021102520013772094_j_spma-2019-0014_ref_011_w2aab3b7c28b1b6b1ab1ac11Aa","doi-asserted-by":"crossref","unstructured":"[11] Z. Stani\u0107, Inequalities for Graph Eigenvalues, Cambridge University Press, Cambridge, 2015.","DOI":"10.1017\/CBO9781316341308"}],"container-title":["Special Matrices"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.degruyter.com\/view\/j\/spma.2019.7.issue-1\/spma-2019-0014\/spma-2019-0014.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2019-0014\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2019-0014\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,25]],"date-time":"2021-10-25T20:08:34Z","timestamp":1635192514000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/spma-2019-0014\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1,1]]},"references-count":11,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2019,9,3]]},"published-print":{"date-parts":[[2019,1,1]]}},"alternative-id":["10.1515\/spma-2019-0014"],"URL":"https:\/\/doi.org\/10.1515\/spma-2019-0014","relation":{},"ISSN":["2300-7451"],"issn-type":[{"value":"2300-7451","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1,1]]}}}