{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T06:14:22Z","timestamp":1764828862922,"version":"3.41.2"},"reference-count":14,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T00:00:00Z","timestamp":1620000000000},"content-version":"vor","delay-in-days":122,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Key Scientific Research Projects of Colleges and Universities in Anhui Province","award":["KJ2018A0903","ORIC\/FEAS-11"],"award-info":[{"award-number":["KJ2018A0903","ORIC\/FEAS-11"]}]},{"name":"Riphah International University","award":["KJ2018A0903","ORIC\/FEAS-11"],"award-info":[{"award-number":["KJ2018A0903","ORIC\/FEAS-11"]}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2021,1]]},"abstract":"<jats:p>Let <jats:italic>G<\/jats:italic> = (<jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>), <jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>)) be a molecular graph, where <jats:italic>V<\/jats:italic>(<jats:italic>G<\/jats:italic>) and <jats:italic>E<\/jats:italic>(<jats:italic>G<\/jats:italic>) are the sets of vertices (atoms) and edges (bonds). A topological index of a molecular graph is a numerical quantity which helps to predict the chemical\/physical properties of the molecules. The Wiener, Wiener polarity, and the terminal Wiener indices are the distance\u2010based topological indices. In this paper, we described a linear time algorithm (LTA) that computes the Wiener index for acyclic graphs and extended this algorithm for unicyclic graphs. The same algorithms are modified to compute the terminal Wiener index and the Wiener polarity index. All these algorithms compute the indices in time <jats:italic>O<\/jats:italic>(<jats:italic>n<\/jats:italic>).<\/jats:p>","DOI":"10.1155\/2021\/6663306","type":"journal-article","created":{"date-parts":[[2021,5,3]],"date-time":"2021-05-03T23:35:34Z","timestamp":1620084934000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Algorithms for Computing Wiener Indices of Acyclic and Unicyclic Graphs"],"prefix":"10.1155","volume":"2021","author":[{"given":"Bo","family":"Bi","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5715-9299","authenticated-orcid":false,"given":"Muhammad Kamran","family":"Jamil","sequence":"additional","affiliation":[]},{"given":"Khawaja","family":"Muhammad Fahd","sequence":"additional","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8928-6073","authenticated-orcid":false,"given":"Tian-Le","family":"Sun","sequence":"additional","affiliation":[]},{"given":"Imran","family":"Ahmad","sequence":"additional","affiliation":[]},{"given":"Lei","family":"Ding","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2021,5,3]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/2014\/06\/p06006"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1049\/iet-cta.2016.1237"},{"key":"e_1_2_7_3_2","article-title":"Structural determination of paraffin boiling points","volume":"1","author":"Wiener H.","year":"1947","journal-title":"Journal of the American Chemical Society"},{"key":"e_1_2_7_4_2","unstructured":"BonchevD. MekenyanO. Proti\u0107G. andTrinajsti\u0107N. Journal of Chromatography 1979 176."},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9673(00)81252-2"},{"key":"e_1_2_7_6_2","article-title":"The dependence of physico-chemical properties on topological factors","volume":"72","author":"Rouvray D. H.","year":"1976","journal-title":"South African Journal of Science"},{"key":"e_1_2_7_7_2","article-title":"Novel applications of topological indices","volume":"41","author":"Rouvray D. 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Wiener indices of spiro and polyphenyl hexagonal 4 chains Mathematical and Computer Modelling 2012 55 no. 3-4 634\u2013644.","DOI":"10.1016\/j.mcm.2011.08.037"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s11671-007-9051-y"},{"key":"e_1_2_7_13_2","first-page":"665","article-title":"On some algorithms for computing topological indices of chemical graphs","volume":"78","author":"Ili\u2018c M.","year":"2017","journal-title":"MATCH Communications in Mathematical and in Computer"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1002\/jcc.540060613"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6663306.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2021\/6663306.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2021\/6663306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T22:00:17Z","timestamp":1723240817000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2021\/6663306"}},"subtitle":[],"editor":[{"given":"Atif","family":"Khan","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2021,1]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,1]]}},"alternative-id":["10.1155\/2021\/6663306"],"URL":"https:\/\/doi.org\/10.1155\/2021\/6663306","archive":["Portico"],"relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2021,1]]},"assertion":[{"value":"2020-12-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-04-21","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-05-03","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"6663306"}}