{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T09:06:31Z","timestamp":1775466391863,"version":"3.50.1"},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"5","license":[{"start":{"date-parts":[[2016,6,21]],"date-time":"2016-06-21T00:00:00Z","timestamp":1466467200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2016,9]]},"abstract":"<jats:p>It is proved that the median eigenvalues of every connected bipartite graph <jats:italic>G<\/jats:italic> of maximum degree at most three belong to the interval [\u22121, 1] with a single exception of the Heawood graph, whose median eigenvalues are <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0963548316000201_inline1\"\/><jats:tex-math>$\\pm\\sqrt{2}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. Moreover, if <jats:italic>G<\/jats:italic> is not isomorphic to the Heawood graph, then a positive fraction of its median eigenvalues lie in the interval [\u22121, 1]. This surprising result has been motivated by the problem about HOMO-LUMO separation that arises in mathematical chemistry.<\/jats:p>","DOI":"10.1017\/s0963548316000201","type":"journal-article","created":{"date-parts":[[2016,6,21]],"date-time":"2016-06-21T06:36:09Z","timestamp":1466490969000},"page":"768-790","source":"Crossref","is-referenced-by-count":10,"title":["Median Eigenvalues of Bipartite Subcubic Graphs"],"prefix":"10.1017","volume":"25","author":[{"given":"BOJAN","family":"MOHAR","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2016,6,21]]},"reference":[{"key":"S0963548316000201_ref5","doi-asserted-by":"crossref","first-page":"99","DOI":"10.26493\/1855-3974.180.65e","article-title":"HL-index of a graph.","volume":"5","author":"Jakli\u010d","year":"2012","journal-title":"Ars Math. Contemp."},{"key":"S0963548316000201_ref4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9"},{"key":"S0963548316000201_ref6","first-page":"79","article-title":"Median eigenvalues of bipartite planar graphs.","volume":"70","author":"Mohar","year":"2013","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"S0963548316000201_ref7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2014.12.001"},{"key":"S0963548316000201_ref2","first-page":"513","article-title":"HOMO-LUMO maps for fullerenes.","volume":"57","author":"Fowler","year":"2010","journal-title":"Acta Chim. Slov."},{"key":"S0963548316000201_ref3","first-page":"373","article-title":"HOMO-LUMO maps for chemical graphs.","volume":"64","author":"Fowler","year":"2010","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"S0963548316000201_ref1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-70982-1"}],"container-title":["Combinatorics, Probability and Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0963548316000201","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,18]],"date-time":"2019-04-18T20:04:45Z","timestamp":1555617885000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0963548316000201\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,21]]},"references-count":7,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2016,9]]}},"alternative-id":["S0963548316000201"],"URL":"https:\/\/doi.org\/10.1017\/s0963548316000201","relation":{},"ISSN":["0963-5483","1469-2163"],"issn-type":[{"value":"0963-5483","type":"print"},{"value":"1469-2163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,6,21]]}}}