{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,11]],"date-time":"2026-10-11T20:15:30Z","timestamp":1791749730543,"version":"4.3.4"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"DOI":"10.13039\/501100001409","name":"Department of Science and Technology, Ministry of Science and Technology","doi-asserted-by":"publisher","award":["MTR\/2017\/000084"],"award-info":[{"award-number":["MTR\/2017\/000084"]}],"id":[{"id":"10.13039\/501100001409","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,4]]},"abstract":"<jats:p> Consider a simple graph [Formula: see text] of order [Formula: see text] and size [Formula: see text] having Laplacian eigenvalues [Formula: see text]. Let [Formula: see text] be the sum of [Formula: see text] largest Laplacian eigenvalues of [Formula: see text]. Brouwer conjectured that [Formula: see text] for all [Formula: see text]. We obtain an upper bound for [Formula: see text] in terms of the clique number [Formula: see text], the number of vertices [Formula: see text] and the non-negative integers [Formula: see text] associated to the structure of the graph [Formula: see text]. We show that the Brouwer\u2019s conjecture holds true for some new families of graphs. We use the same technique to prove that the Brouwer\u2019s conjecture is true for a subclass of split graphs (It is already known that Brouwer\u2019s conjecture holds for split graphs). <\/jats:p>","DOI":"10.1142\/s1793830919500289","type":"journal-article","created":{"date-parts":[[2019,3,3]],"date-time":"2019-03-03T22:30:43Z","timestamp":1551652243000},"page":"1950028","source":"Crossref","is-referenced-by-count":16,"title":["Upper bounds for the sum of Laplacian eigenvalues of a graph and Brouwer\u2019s conjecture"],"prefix":"10.1142","volume":"11","author":[{"given":"Hilal A.","family":"Ganie","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar, Kashmir 196006, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1137-517X","authenticated-orcid":false,"given":"S.","family":"Pirzada","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar, Kashmir 196006, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Rezwan","family":"Ul Shaban","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kashmir, Srinagar, Kashmir 196006, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"X.","family":"Li","sequence":"additional","affiliation":[{"name":"Center for Combinatorics, Nankai University, Tianjin 300071, P. 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