{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,1]],"date-time":"2024-08-01T02:55:11Z","timestamp":1722480911878},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,9]]},"abstract":"<jats:p> Let G<jats:sub>w<\/jats:sub> be a weighted graph. The number of the positive, negative and zero eigenvalues in the spectrum of G<jats:sub>w<\/jats:sub> are called positive inertia index, negative inertia index and nullity of G<jats:sub>w<\/jats:sub>, and denoted by i<jats:sub>+<\/jats:sub>(G<jats:sub>w<\/jats:sub>), i<jats:sub>-<\/jats:sub>(G<jats:sub>w<\/jats:sub>), i<jats:sub>0<\/jats:sub>(G<jats:sub>w<\/jats:sub>), respectively. In this paper, sharp lower bound on the positive (respectively, negative) inertia index of weighted bicyclic graphs of order n with pendant vertices is obtained. Moreover, all the weighted bicyclic graphs of order n with at most two positive, two negative and at least n - 4 zero eigenvalues are identified, respectively. <\/jats:p>","DOI":"10.1142\/s1793830914500426","type":"journal-article","created":{"date-parts":[[2014,3,27]],"date-time":"2014-03-27T09:40:20Z","timestamp":1395913220000},"page":"1450042","source":"Crossref","is-referenced-by-count":2,"title":["The extremal problems on the inertia of weighted bicyclic graphs"],"prefix":"10.1142","volume":"06","author":[{"given":"Shibing","family":"Deng","sequence":"first","affiliation":[{"name":"Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China"}]},{"given":"Shuchao","family":"Li","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China"}]},{"given":"Feifei","family":"Song","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,6,16]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2013.04.032"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02941924"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2008.04.013"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2009.01.007"},{"key":"rf6","first-page":"245","volume":"397","author":"Fan Y. Z.","journal-title":"Linear Algebra Appl."},{"key":"rf7","volume-title":"An Atlas of Fullerenes","author":"Fowler P. W.","year":"1995"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/S0095-8956(02)00041-2"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0024-3795(99)00042-7"},{"key":"rf10","first-page":"49","volume":"42","author":"Gutman I.","journal-title":"Top. Curr. Chem."},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.12.007"},{"key":"rf12","volume-title":"The Theory of Matrices","author":"Lancaster P.","year":"1985"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2008.04.037"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1063\/1.1747618"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2012.07.014"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.06.017"},{"key":"rf18","first-page":"212","volume":"408","author":"Tan X. Z.","journal-title":"Linear Algebra Appl."},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2012.09.031"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500426","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T17:16:07Z","timestamp":1565111767000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500426"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,6,16]]},"references-count":17,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2014,6,16]]},"published-print":{"date-parts":[[2014,9]]}},"alternative-id":["10.1142\/S1793830914500426"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500426","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,6,16]]}}}