{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:15:49Z","timestamp":1758824149849,"version":"3.37.3"},"reference-count":24,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2020,10,4]],"date-time":"2020-10-04T00:00:00Z","timestamp":1601769600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,10,4]],"date-time":"2020-10-04T00:00:00Z","timestamp":1601769600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11901525","11801512"],"award-info":[{"award-number":["11901525","11801512"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY20A010005"],"award-info":[{"award-number":["LY20A010005"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Research Foundation of the Korean government","award":["2017R1D1A1B03028642"],"award-info":[{"award-number":["2017R1D1A1B03028642"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,12]]},"DOI":"10.1007\/s40314-020-01340-2","type":"journal-article","created":{"date-parts":[[2020,10,4]],"date-time":"2020-10-04T17:02:30Z","timestamp":1601830950000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["On the normalized Laplacian spectral radii of a graph and its line graph"],"prefix":"10.1007","volume":"39","author":[{"given":"Shaowei","family":"Sun","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2576-160X","authenticated-orcid":false,"given":"Kinkar Chandra","family":"Das","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,10,4]]},"reference":[{"key":"1340_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-349-03521-2","volume-title":"Graph theory with applications","author":"JA Bondy","year":"1976","unstructured":"Bondy JA, Murty USR (1976) Graph theory with applications. Macmillan Press, New York"},{"key":"1340_CR2","unstructured":"Butler S (2008) Eigenvalues and structures of graphs. Ph.D. dissertation, University of California, San Diego"},{"key":"1340_CR3","unstructured":"Cavers M (2010) The normalized Laplacian matrix and general Randi\u0107 index of graphs. Ph.D. dissertation, University of Regina"},{"key":"1340_CR4","doi-asserted-by":"publisher","first-page":"75","DOI":"10.1016\/0166-218X(92)90206-P","volume":"36","author":"L Cai","year":"1992","unstructured":"Cai L, Ellis JA (1992) Edge colouring line graphs of unicyclic graphs. Discrete Appl Math 36:75\u201382","journal-title":"Discrete Appl Math"},{"key":"1340_CR5","volume-title":"Spectral graph theory","author":"FK Chung","year":"1997","unstructured":"Chung FK (1997) Spectral graph theory. American Mathematical Society, Providence"},{"key":"1340_CR6","doi-asserted-by":"publisher","first-page":"237","DOI":"10.13001\/1081-3810.3263","volume":"29","author":"KC Das","year":"2016","unstructured":"Das KC, Sun S (2016) Extremal graph on normalized Laplacian spectral radius and energy. Electron J Linear Algebra 29:237\u2013253","journal-title":"Electron J Linear Algebra"},{"key":"1340_CR7","first-page":"333","volume-title":"The average impedance of an electrical network, In Contributions to Applied Mechanics (Reissner Aniversary Volume)","author":"RM Foster","year":"1949","unstructured":"Foster RM (1949) The average impedance of an electrical network, In Contributions to Applied Mechanics (Reissner Aniversary Volume). Edwards Brothers, Ann Arbor, pp 333\u2013340"},{"issue":"11","key":"1340_CR8","doi-asserted-by":"publisher","first-page":"2177","DOI":"10.1080\/03081087.2016.1143912","volume":"64","author":"JM Guo","year":"2016","unstructured":"Guo JM, Li J, Shiu WC (2016) Effects on the normalized Laplacian spectral radius of non-bipartite graphs under perturbation and their applications. Linear Multilinear Algebra 64(11):2177\u20132187","journal-title":"Linear Multilinear Algebra"},{"issue":"1","key":"1340_CR9","doi-asserted-by":"publisher","first-page":"77","DOI":"10.1007\/s40840-015-0241-y","volume":"39","author":"JM Guo","year":"2016","unstructured":"Guo JM, Li J, Shiu WC (2016) The largest normalized Laplacian spectral radius of non-bipartite graphs. Bull Malays Math Sci Soc 39(1):77\u201387","journal-title":"Bull Malays Math Sci Soc"},{"key":"1340_CR10","doi-asserted-by":"publisher","first-page":"1312","DOI":"10.1016\/j.laa.2010.05.009","volume":"433","author":"I Gutman","year":"2010","unstructured":"Gutman I, Robbiano M, Martins EA, Cardoso DM, Medina L, Rojo O (2010) Energy of line graphs. Linear Algebra Appl 433:1312\u20131323","journal-title":"Linear Algebra Appl"},{"key":"1340_CR11","doi-asserted-by":"publisher","first-page":"197","DOI":"10.1016\/0095-8956(74)90065-3","volume":"16","author":"AK Kelmans","year":"1974","unstructured":"Kelmans AK, Chelnokov VM (1974) A certain polynomial of a graph and graphs with an extremal number of trees. J Combin Theory B 16:197\u2013214","journal-title":"J Combin Theory B"},{"key":"1340_CR12","doi-asserted-by":"publisher","first-page":"81","DOI":"10.1007\/BF01164627","volume":"12","author":"DJ Klein","year":"1993","unstructured":"Klein DJ, Randi\u0107 M (1993) Resistance distance. J Math Chem 12:81\u201395","journal-title":"J Math Chem"},{"key":"1340_CR13","first-page":"1","volume":"316","author":"J Li","year":"2014","unstructured":"Li J, Guo J-M, Shiu WC (2014) Bounds on normalized Laplacian eigenvalues of graphs. J Inequalities Appl 316:1\u20138","journal-title":"J Inequalities Appl"},{"key":"1340_CR14","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1016\/j.laa.2019.08.004","volume":"582","author":"EI Milovanovi\u0107","year":"2019","unstructured":"Milovanovi\u0107 EI, Mateji\u0107 MM, Milovanovi\u0107 I\u017d (2019) On the normalized Laplacian spectral radius, Laplacian incidence energy and Kemeny\u2019s constant. Linear Algebra Appl 582:181\u2013196","journal-title":"Linear Algebra Appl"},{"key":"1340_CR15","doi-asserted-by":"crossref","unstructured":"Milovanovi\u0107 EI, Milovanovi\u0107 I\u017d (2015) Remarks on bounds of normalized Laplacian Eigenvalues of graphs. arXiv:1506.05762v1","DOI":"10.1007\/s10587-015-0191-4"},{"key":"1340_CR16","doi-asserted-by":"publisher","first-page":"381","DOI":"10.1023\/B:MCAP.0000045086.76839.54","volume":"6","author":"JL Palacios","year":"2004","unstructured":"Palacios JL (2004) Foster\u2019s formulas via probability and the Kirchhoff Index. Methodol Comput Appl Probab 6:381\u2013387","journal-title":"Methodol Comput Appl Probab"},{"key":"1340_CR17","doi-asserted-by":"publisher","first-page":"58","DOI":"10.1016\/j.laa.2006.08.030","volume":"422","author":"L Shi","year":"2007","unstructured":"Shi L (2007) Spectral radii of a graph and its line graph. Linear Algebra Appl 422:58\u201366","journal-title":"Linear Algebra Appl"},{"key":"1340_CR18","first-page":"9","volume":"22","author":"I Schur","year":"1923","unstructured":"Schur I (1923) \u00fcber eine Klasse von Mittelbildungen mit Anwendungen auf die Determinantentheorie. Sitzungsber Berl Math Ges 22:9\u201320","journal-title":"Sitzungsber Berl Math Ges"},{"key":"1340_CR19","unstructured":"Stein WA (2015) Sage mathematics software (version 6.8). The Sage Development Team. http:\/\/www.sagemath.org"},{"key":"1340_CR20","doi-asserted-by":"publisher","first-page":"109","DOI":"10.26493\/1855-3974.499.103","volume":"9","author":"D Stevanovi\u0107","year":"2015","unstructured":"Stevanovi\u0107 D, Gutman I, Rehman MU (2015) On spectral radius and energy of complete multipartite graphs. Ars Math Contemp 9:109\u2013113","journal-title":"Ars Math Contemp"},{"issue":"1","key":"1340_CR21","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1080\/03081087.2018.1498827","volume":"68","author":"S Sun","year":"2020","unstructured":"Sun S, Das KC (2020) Normalized Laplacian eigenvalues with chromatic number and independence number of graphs. Linear Multilinear Algebra 68(1):63\u201380","journal-title":"Linear Multilinear Algebra"},{"issue":"10","key":"1340_CR22","doi-asserted-by":"publisher","first-page":"1741","DOI":"10.1080\/00207160.2015.1073722","volume":"93","author":"K Xu","year":"2016","unstructured":"Xu K, Das KC, Zhang XD (2016) Ordering connected graphs by their Kirchhoff indices. Int J Comput Math 93(10):1741\u20131755","journal-title":"Int J Comput Math"},{"key":"1340_CR23","volume-title":"Distance, symmetry, and topology in carbon nanomaterials","author":"Z Yarahmadi","year":"2016","unstructured":"Yarahmadi Z (2016) Study of the bipartite edge frustration of graphs. In: Ashrafi A, Diudea M (eds) Distance, symmetry, and topology in carbon nanomaterials. Springer, New York"},{"key":"1340_CR24","first-page":"191","volume":"72","author":"XD Zhang","year":"2004","unstructured":"Zhang XD (2004) On the Laplacian spectra of graphs. ARS Comb 72:191\u2013198","journal-title":"ARS Comb"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01340-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01340-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01340-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,11,22]],"date-time":"2022-11-22T03:04:38Z","timestamp":1669086278000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01340-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,4]]},"references-count":24,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["1340"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01340-2","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2020,10,4]]},"assertion":[{"value":"5 June 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"23 September 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"25 September 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"283"}}