{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,15]],"date-time":"2025-03-15T04:07:51Z","timestamp":1742011671804,"version":"3.38.0"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2025,1,25]],"date-time":"2025-01-25T00:00:00Z","timestamp":1737763200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,25]],"date-time":"2025-01-25T00:00:00Z","timestamp":1737763200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271439"],"award-info":[{"award-number":["12271439"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Practice and Innovation Funds for Graduate Students of Northwestern Polytechnical University","award":["PF2024114"],"award-info":[{"award-number":["PF2024114"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2025,4]]},"DOI":"10.1007\/s40314-025-03095-0","type":"journal-article","created":{"date-parts":[[2025,1,25]],"date-time":"2025-01-25T06:48:11Z","timestamp":1737787691000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Brouwer type conjecture for the eigenvalues of distance Laplacian matrix of a graph"],"prefix":"10.1007","volume":"44","author":[{"given":"Yuwei","family":"Zhou","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6160-1761","authenticated-orcid":false,"given":"Ligong","family":"Wang","sequence":"additional","affiliation":[]},{"given":"Yirui","family":"Chai","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2025,1,25]]},"reference":[{"key":"3095_CR1","doi-asserted-by":"publisher","first-page":"2423","DOI":"10.1080\/03081087.2019.1679074","volume":"69","author":"A Alhevaz","year":"2021","unstructured":"Alhevaz A, Baghipur M, Ganie H, Pirzada S (2021) Brouwer type conjecture for the eigenvalues of distance signless Laplacian matrix of a graph. Linear Multilinear Algebra 69:2423\u20132440","journal-title":"Linear Multilinear Algebra"},{"key":"3095_CR2","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1016\/j.laa.2013.02.030","volume":"439","author":"M Aouchiche","year":"2013","unstructured":"Aouchiche M, Hansen P (2013) Two Laplacians for the distance matrix of a graph. Linear Algebra Appl 439:21\u201333","journal-title":"Linear Algebra Appl"},{"key":"3095_CR3","doi-asserted-by":"publisher","first-page":"751","DOI":"10.1007\/s10587-014-0129-2","volume":"64","author":"M Aouchiche","year":"2014","unstructured":"Aouchiche M, Hansen P (2014a) Some properties of the distance Laplacian eigenvalues of a graph. Czechoslovak Math J 64:751\u2013761","journal-title":"Czechoslovak Math J"},{"key":"3095_CR4","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1016\/j.laa.2014.06.010","volume":"458","author":"M Aouchiche","year":"2014","unstructured":"Aouchiche M, Hansen P (2014b) Distance spectra of graphs: a survey. Linear Algebra Appl 458:301\u2013386","journal-title":"Linear Algebra Appl"},{"key":"3095_CR5","doi-asserted-by":"publisher","first-page":"4463","DOI":"10.1090\/S0002-9947-2011-05393-6","volume":"363","author":"H Bai","year":"2011","unstructured":"Bai H (2011) The Grone\u2013Merris conjecture. Trans Am Math Soc 363:4463\u20134474","journal-title":"Trans Am Math Soc"},{"key":"3095_CR6","volume-title":"Spectra of graphs","author":"A Brouwer","year":"2011","unstructured":"Brouwer A, Haemers W (2011) Spectra of graphs. Springer, Berlin"},{"key":"3095_CR7","doi-asserted-by":"publisher","first-page":"327","DOI":"10.1016\/j.laa.2018.08.003","volume":"557","author":"X Chen","year":"2018","unstructured":"Chen X (2018) Improved results on Brouwers conjecture for sum of the Laplacian eigenvalues of a graph. Linear Algebra Appl 557:327\u2013338","journal-title":"Linear Algebra Appl"},{"key":"3095_CR8","doi-asserted-by":"publisher","first-page":"3672","DOI":"10.1016\/j.laa.2012.01.007","volume":"436","author":"Z Du","year":"2012","unstructured":"Du Z, Zhou B (2012) Upper bounds for the sum of Laplacian eigenvalues of graphs. Linear Algebra Appl 436:3672\u20133683","journal-title":"Linear Algebra Appl"},{"key":"3095_CR9","doi-asserted-by":"publisher","first-page":"283","DOI":"10.21136\/CMJ.1976.101401","volume":"26","author":"R Entringer","year":"1976","unstructured":"Entringer R, Jackson D, Snyder D (1976) Distance in graphs. Czechoslovak Math J 26:283\u2013296","journal-title":"Czechoslovak Math J"},{"key":"3095_CR10","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1137\/15M1013262","volume":"37","author":"E Fritscher","year":"2016","unstructured":"Fritscher E, Trevisan V (2016) Exploring symmetries to decompose matrices and graphs preserving the spectrum. SIAM J Matrix Anal Appl 37:260\u2013289","journal-title":"SIAM J Matrix Anal Appl"},{"key":"3095_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1142\/S1793830919500289","volume":"11","author":"H Ganie","year":"2019","unstructured":"Ganie H, Pirzada S, Ul Shaban R, Li X (2019) Upper bounds for the sum of Laplacian eigenvalues of a graph and Brouwer\u2019s conjecture. Discrete Math Algorithms Appl 11:1\u201315","journal-title":"Discrete Math Algorithms Appl"},{"key":"3095_CR12","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/j.laa.2019.11.020","volume":"588","author":"H Ganie","year":"2020","unstructured":"Ganie H, Pirzada S, Rather B, Trevisan V (2020) Further developments on Brouwer\u2019s conjecture for the sum of Laplacian eigenvalues of graphs. Linear Algebra Appl 588:1\u201318","journal-title":"Linear Algebra Appl"},{"key":"3095_CR13","first-page":"13","volume":"36","author":"H Ganie","year":"2021","unstructured":"Ganie H, Pirzada S, Rather B, Ul Shaban R (2021a) On Laplacian eigenvalues of graphs and Brouwer\u2019s conjecture. J Ramanujan Math Soc 36:13\u201321","journal-title":"J Ramanujan Math Soc"},{"key":"3095_CR14","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/s00009-020-01676-3","volume":"18","author":"H Ganie","year":"2021","unstructured":"Ganie H, Pirzada S, Trevisan V (2021b) On the sum of $$k$$ largest Laplacian eigenvalues of a graph and clique number. Mediterr J Math 18:1\u201313","journal-title":"Mediterr J Math"},{"key":"3095_CR15","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-0163-9","volume-title":"Algebraic graph theory","author":"C Godsil","year":"2001","unstructured":"Godsil C, Royle G (2001) Algebraic graph theory. Springer, New York"},{"key":"3095_CR16","doi-asserted-by":"publisher","first-page":"221","DOI":"10.1137\/S0895480191222653","volume":"7","author":"R Grone","year":"1994","unstructured":"Grone R, Merris R (1994) The Laplacian spectrum of a graph II. SIAM J Discrete Math 7:221\u2013229","journal-title":"SIAM J Discrete Math"},{"key":"3095_CR17","doi-asserted-by":"publisher","first-page":"2214","DOI":"10.1016\/j.laa.2009.03.038","volume":"432","author":"W Haemers","year":"2010","unstructured":"Haemers W, Mohammadian A, Tayfeh-Rezaie B (2010) On the sum of Laplacian eigenvalues of graphs. Linear Algebra Appl 432:2214\u20132221","journal-title":"Linear Algebra Appl"},{"key":"3095_CR18","first-page":"29","volume":"50","author":"H Lin","year":"2021","unstructured":"Lin H, Shu J, Xue J, Zhang Y (2021) A survey on distance spectra of graphs. Adv Math 50:29\u201376","journal-title":"Adv Math"},{"key":"3095_CR19","unstructured":"Mayank (2010) On variants of the Grone\u2013Merris conjecture. Master\u2019s thesis, Eindhoven University of Technology"},{"key":"3095_CR20","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1016\/j.laa.2014.07.025","volume":"460","author":"M Nath","year":"2014","unstructured":"Nath M, Paul S (2014) On the distance Laplacian spectra of graphs. Linear Algebra Appl 460:97\u2013110","journal-title":"Linear Algebra Appl"},{"key":"3095_CR21","doi-asserted-by":"publisher","first-page":"454","DOI":"10.1016\/j.laa.2015.08.032","volume":"486","author":"S Pirzada","year":"2015","unstructured":"Pirzada S, Ganie H (2015) On the Laplacian eigenvalues of a graph and Laplacian energy. Linear Algebra Appl 486:454\u2013468","journal-title":"Linear Algebra Appl"},{"key":"3095_CR22","doi-asserted-by":"publisher","first-page":"44","DOI":"10.1016\/j.laa.2021.04.021","volume":"625","author":"S Pirzada","year":"2021","unstructured":"Pirzada S, Khan S (2021) On distance Laplacian spectral radius and chromatic number of graphs. Linear Algebra Appl 625:44\u201354","journal-title":"Linear Algebra Appl"},{"issue":"213","key":"3095_CR23","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1016\/0024-3795(94)90399-9","volume":"212","author":"W So","year":"1994","unstructured":"So W (1994) Commutativity and spectra of Hermitian matrices. Linear Algebra Appl 212(213):121\u2013129","journal-title":"Linear Algebra Appl"},{"key":"3095_CR24","doi-asserted-by":"publisher","first-page":"60","DOI":"10.1016\/j.mcm.2011.12.047","volume":"56","author":"S Wang","year":"2012","unstructured":"Wang S, Huang Y, Liu B (2012) On a conjecture for the sum of Laplacian eigenvalues. Math Comput Model 56:60\u201368","journal-title":"Math Comput Model"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03095-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-025-03095-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-025-03095-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,3,14]],"date-time":"2025-03-14T06:08:13Z","timestamp":1741932493000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-025-03095-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,25]]},"references-count":24,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,4]]}},"alternative-id":["3095"],"URL":"https:\/\/doi.org\/10.1007\/s40314-025-03095-0","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2025,1,25]]},"assertion":[{"value":"27 June 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 December 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 January 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 January 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"138"}}