{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T11:16:45Z","timestamp":1774437405917,"version":"3.50.1"},"reference-count":17,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2019,8,9]],"date-time":"2019-08-09T00:00:00Z","timestamp":1565308800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The Hosoya index of a graph is defined by the total number of the matchings of the graph. In this paper, we determine the maximum Hosoya index of unicyclic graphs with n vertices and diameter 3 or 4. Our results somewhat answer a question proposed by Wagner and Gutman in 2010 for unicyclic graphs with small diameter.<\/jats:p>","DOI":"10.3390\/sym11081034","type":"journal-article","created":{"date-parts":[[2019,8,9]],"date-time":"2019-08-09T11:11:31Z","timestamp":1565349091000},"page":"1034","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["The Maximum Hosoya Index of Unicyclic Graphs with Diameter at Most Four"],"prefix":"10.3390","volume":"11","author":[{"given":"Weijun","family":"Liu","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Central South University New Campus, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jingwen","family":"Ban","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University New Campus, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lihua","family":"Feng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Central South University New Campus, Changsha 410083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tao","family":"Cheng","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Shandong Normal University, Jinan 250014, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Frank","family":"Emmert-Streib","sequence":"additional","affiliation":[{"name":"Predictive Society and Data Analytics Lab Faculty of Information Technolgy and Communication Sciences, Tampere University, 33100 Tampere, Finland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matthias","family":"Dehmer","sequence":"additional","affiliation":[{"name":"School of Management, University of Applied Sciences Upper Austria, 4400 Steyr, Austria"},{"name":"Department of Biomedical Computer Science and Mechatronics UMIT, 6060 Hall in Tyrol, Austria"},{"name":"College of Articial Intelligence, Nankai University, Tianjin 300350, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,9]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Balaban, A.T., and Devillers, J. (1999). Information-theoretic indices of neighborhood complexity and their applications. Topological Indices and Related Descriptors in QSAR and QSPR, Gordon and Breach Science Publishers.","DOI":"10.1201\/9781482296945"},{"key":"ref_2","first-page":"331","article-title":"Interrelationship of major topological indices evidenced by clustering","volume":"77","author":"Basak","year":"2014","journal-title":"Croat. Chem. Acta"},{"key":"ref_3","first-page":"501","article-title":"Molecular topology and narcosis","volume":"33","author":"Basak","year":"1983","journal-title":"Arzeim. Forsch. Drug Des."},{"key":"ref_4","unstructured":"Todeschini, R., Consonni, V., and Mannhold, R. (2002). Handbook of Molecular Descriptors, Wiley-VCH."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2332","DOI":"10.1246\/bcsj.44.2332","article-title":"Topological index. 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Chem."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"423","DOI":"10.1007\/s10910-006-9112-y","article-title":"On extremal unicyclic molecular graphs with prescribed girth and minimal Hosoya index","volume":"42","author":"Ou","year":"2007","journal-title":"J. Math. Chem."},{"key":"ref_13","first-page":"629","article-title":"Some extremal unicyclic graphs with respect to Hosoya index and Merrifield-Simmons index","volume":"62","author":"Xu","year":"2009","journal-title":"MATCH Commun. Math. Comput. Chem."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2573","DOI":"10.2298\/FIL1609573Y","article-title":"The largest n \u2212 1 Hosoya indices of unicyclic graphs","volume":"30","author":"Yu","year":"2016","journal-title":"Filomat"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2499","DOI":"10.1016\/j.camwa.2008.05.020","article-title":"The largest Hosoya index of (n, n + 1)-graphs","volume":"56","author":"Deng","year":"2006","journal-title":"Comput. Math. Appl."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"323","DOI":"10.1007\/s10440-010-9575-5","article-title":"Maxima and minima of the Hosoya index and the Merrifield-Simmons index: A survey of results and techniques","volume":"112","author":"Wagner","year":"2010","journal-title":"Acta Appl. Math."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Bollob\u00e1s, B. (1998). Modern Graph Theory, Springer.","DOI":"10.1007\/978-1-4612-0619-4"}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1034\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:10:05Z","timestamp":1760188205000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/8\/1034"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,9]]},"references-count":17,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2019,8]]}},"alternative-id":["sym11081034"],"URL":"https:\/\/doi.org\/10.3390\/sym11081034","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,8,9]]}}}