{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:55:21Z","timestamp":1740142521299,"version":"3.37.3"},"reference-count":17,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T00:00:00Z","timestamp":1715126400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T00:00:00Z","timestamp":1715126400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2024,6]]},"DOI":"10.1007\/s40314-024-02707-5","type":"journal-article","created":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T19:01:30Z","timestamp":1715194890000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A new characterization of k-trees and some applications"],"prefix":"10.1007","volume":"43","author":[{"given":"Lilian","family":"Markenzon","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5464-8975","authenticated-orcid":false,"given":"Allana S. S.","family":"de Oliveira","sequence":"additional","affiliation":[]},{"given":"Cybele T. M.","family":"Vinagre","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,5,8]]},"reference":[{"key":"2707_CR1","doi-asserted-by":"publisher","unstructured":"Abiad A, Brimkov B, Leshock L, Mart\u00ednez-Rivera X, O S, Song S-Y, Willifor J, (2017) On the wiener index, distance cospectrality and transmission-regular graphs. Discr Appl Math 230:1\u201310. https:\/\/doi.org\/10.1016\/j.dam.2017.07.010","DOI":"10.1016\/j.dam.2017.07.010"},{"issue":"2","key":"2707_CR2","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1016\/S0021-9800(69)80120-1","volume":"6","author":"LW Beineke","year":"1969","unstructured":"Beineke LW, Pippert RE (1969) The number of labeled k-dimensional trees. J Combin Theory 6(2):200\u2013205. https:\/\/doi.org\/10.1016\/S0021-9800(69)80120-1","journal-title":"J Combin Theory"},{"key":"2707_CR3","unstructured":"Biggs N (1993) Algebraic graph theory, 2nd edn. In: Cambridge mathematical library. Cambridge University Press, Cambridge"},{"key":"2707_CR4","doi-asserted-by":"publisher","unstructured":"Blair JR, Peyton B (1993) An introduction to chordal graphs and clique trees: 1\u201329. https:\/\/doi.org\/10.1007\/978-1-4613-8369-7_1","DOI":"10.1007\/978-1-4613-8369-7_1"},{"issue":"1","key":"2707_CR5","first-page":"12","volume":"87","author":"Z Che","year":"2023","unstructured":"Che Z (2023) (k+ 1)-line graphs of k-trees. Austr J Combin 87(1):12\u201323","journal-title":"Austr J Combin"},{"key":"2707_CR6","doi-asserted-by":"publisher","first-page":"121","DOI":"10.1007\/s13173-011-0048-0","volume":"18","author":"P De Caria","year":"2012","unstructured":"De Caria P, Gutierrez M (2012) Determining what sets of trees can be the clique trees of a chordal graph. J Braz Comput Soc 18:121\u2013128. https:\/\/doi.org\/10.1007\/s13173-011-0048-0","journal-title":"J Braz Comput Soc"},{"key":"2707_CR7","doi-asserted-by":"publisher","unstructured":"Galinier P, Habib M, Paul C (1995) Chordal graphs and their clique graphs. In: International Workshop on Graph-Theoretic Concepts in Computer Science, pp. 358\u2013371 . Springer. https:\/\/doi.org\/10.1007\/3-540-60618-1_88","DOI":"10.1007\/3-540-60618-1_88"},{"key":"2707_CR8","doi-asserted-by":"crossref","unstructured":"Golumbic MC (2004) Algorithmic graph theory and perfect graphs, 2nd edn. In: Annals of discrete mathematics, vol 57. Elsevier Science B.V., Amsterdam","DOI":"10.1016\/S0167-5060(04)80051-7"},{"issue":"5","key":"2707_CR9","doi-asserted-by":"publisher","first-page":"712","DOI":"10.1016\/j.ejc.2011.09.031","volume":"33","author":"M Habib","year":"2012","unstructured":"Habib M, Stacho J (2012) Reduced clique graphs of chordal graphs. Eur J Combin 33(5):712\u2013735. https:\/\/doi.org\/10.1016\/j.ejc.2011.09.031","journal-title":"Eur J Combin"},{"key":"2707_CR10","doi-asserted-by":"crossref","unstructured":"Harary F (1969) Graph theory. Addison-Wesley Publishing Co., CA, London","DOI":"10.21236\/AD0705364"},{"issue":"2","key":"2707_CR11","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/0020-0190(89)90070-7","volume":"31","author":"C-W Ho","year":"1989","unstructured":"Ho C-W, Lee RCT (1989) Counting clique trees and computing perfect elimination schemes in parallel. Inform Process Lett 31(2):61\u201368. https:\/\/doi.org\/10.1016\/0020-0190(89)90070-7","journal-title":"Inform Process Lett"},{"issue":"1\u20133","key":"2707_CR12","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1016\/S0166-218X(00)00336-X","volume":"117","author":"PS Kumar","year":"2002","unstructured":"Kumar PS, Madhavan CV (2002) Clique tree generalization and new subclasses of chordal graphs. Disc Appl Math 117(1\u20133):109\u2013131. https:\/\/doi.org\/10.1016\/S0166-218X(00)00336-X","journal-title":"Disc Appl Math"},{"issue":"1","key":"2707_CR13","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1002\/jgt.3190170108","volume":"17","author":"VB L\u00ea","year":"1993","unstructured":"L\u00ea VB (1993) Perfect k-line graphs and k-total graphs. J Graph Theory 17(1):65\u201373. https:\/\/doi.org\/10.1002\/jgt.3190170108","journal-title":"J Graph Theory"},{"issue":"6","key":"2707_CR14","doi-asserted-by":"publisher","first-page":"683","DOI":"10.1111\/j.1475-3995.2009.00751.x","volume":"17","author":"L Markenzon","year":"2010","unstructured":"Markenzon L, Da Costa Pereira PR (2010) One-phase algorithm for the determination of minimal vertex separators of chordal graphs. International Transactions in Operational Research 17(6):683\u2013690. https:\/\/doi.org\/10.1111\/j.1475-3995.2009.00751.x","journal-title":"International Transactions in Operational Research"},{"issue":"4","key":"2707_CR15","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1016\/j.orl.2013.03.008","volume":"41","author":"L Markenzon","year":"2013","unstructured":"Markenzon L, Waga CFEM, Costa Pereira PR, Friedmann CVP, Lozano ARG (2013) An efficient representation of chordal graphs. Oper Res Lett 41(4):331\u2013335. https:\/\/doi.org\/10.1016\/j.orl.2013.03.008","journal-title":"Oper Res Lett"},{"key":"2707_CR16","doi-asserted-by":"publisher","first-page":"244","DOI":"10.1016\/j.laa.2020.04.008","volume":"614","author":"ASS Oliveira","year":"2021","unstructured":"Oliveira ASS, Freitas MAA, Vinagre CTM, Markenzon L (2021) On $$(k+ 1)$$-line graphs of $$k$$-trees and their nullities. Linear Algebra Appl 614:244\u2013255. https:\/\/doi.org\/10.1016\/j.laa.2020.04.008","journal-title":"Linear Algebra Appl"},{"issue":"3\u20134","key":"2707_CR17","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1016\/0012-365X(74)90042-9","volume":"7","author":"DJ Rose","year":"1974","unstructured":"Rose DJ (1974) On simple characterizations of k-trees. Disc Math 7(3\u20134):317\u2013322. https:\/\/doi.org\/10.1016\/0012-365X(74)90042-9","journal-title":"Disc Math"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02707-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-024-02707-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-024-02707-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T02:07:19Z","timestamp":1718071639000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-024-02707-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5,8]]},"references-count":17,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,6]]}},"alternative-id":["2707"],"URL":"https:\/\/doi.org\/10.1007\/s40314-024-02707-5","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2024,5,8]]},"assertion":[{"value":"28 January 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 March 2024","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"21 March 2024","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 May 2024","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 for this work.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"231"}}