{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,13]],"date-time":"2026-06-13T04:41:26Z","timestamp":1781325686650,"version":"3.54.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T00:00:00Z","timestamp":1649808000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T00:00:00Z","timestamp":1649808000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2022,6]]},"DOI":"10.1007\/s40314-022-01852-z","type":"journal-article","created":{"date-parts":[[2022,4,13]],"date-time":"2022-04-13T20:10:46Z","timestamp":1649880646000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["Extremal problems on Sombor indices of unicyclic graphs with a given diameter"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7606-4842","authenticated-orcid":false,"given":"Hechao","family":"Liu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2022,4,13]]},"reference":[{"key":"1852_CR1","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/j.dam.2021.02.012","volume":"295","author":"MR Alfuraidan","year":"2021","unstructured":"Alfuraidan MR, Das KC, Vetrik T, Selvaraj B (2021) General sum-connectivity index of unicyclic graphs with given diameter. Discret Appl Math 295:39\u201346","journal-title":"Discret Appl Math"},{"key":"1852_CR2","doi-asserted-by":"publisher","first-page":"7","DOI":"10.1016\/j.dam.2021.09.016","volume":"306","author":"MR Alfuraidan","year":"2022","unstructured":"Alfuraidan MR, Das KC, Vetrik T, Selvaraj B (2022) General Randi\u0107 index of unicyclic graphs with given diameter. Discret Appl Math 306:7\u201316","journal-title":"Discret Appl Math"},{"key":"1852_CR3","first-page":"715","volume":"86","author":"S Alikhani","year":"2021","unstructured":"Alikhani S, Ghanbari N (2021) Sombor index of polymers. MATCH Commun Math Comput Chem 86:715\u2013728","journal-title":"MATCH Commun Math Comput Chem"},{"key":"1852_CR4","doi-asserted-by":"publisher","first-page":"23","DOI":"10.46793\/match.87-1.023C","volume":"87","author":"H Chen","year":"2022","unstructured":"Chen H, Li W, Wang J (2022) Extremal values on the Sombor index of trees. MATCH Commun Math Comput Chem 87:23\u201349","journal-title":"MATCH Commun Math Comput Chem"},{"key":"1852_CR5","doi-asserted-by":"publisher","first-page":"1098","DOI":"10.1007\/s10910-021-01232-8","volume":"59","author":"R Cruz","year":"2021","unstructured":"Cruz R, Rada J (2021) Extremal values of the Sombor index in unicyclic and bicyclic graphs. J Math Chem 59:1098\u20131116","journal-title":"J Math Chem"},{"key":"1852_CR6","first-page":"#126018","volume":"399","author":"R Cruz","year":"2021","unstructured":"Cruz R, Gutman I, Rada J (2021) Sombor index of chemical graphs. Appl Math Comput 399:#126018","journal-title":"Appl Math Comput"},{"key":"1852_CR7","doi-asserted-by":"crossref","unstructured":"Deng H, Tang Z, Wu R (2021) Molecular trees with extremal values of Sombor indices. Int J Quantum Chem 121:#e26622","DOI":"10.1002\/qua.26622"},{"key":"1852_CR8","first-page":"1","volume":"7","author":"T Do\u0161li\u0107","year":"2021","unstructured":"Do\u0161li\u0107 T, R\u00e9ti T, Ali A (2021) On the structure of graphs with integer Sombor indices. Discret Math Lett 7:1\u20134","journal-title":"Discret Math Lett"},{"key":"1852_CR9","doi-asserted-by":"publisher","first-page":"#e26740","DOI":"10.1002\/qua.26740","volume":"121","author":"X Fang","year":"2021","unstructured":"Fang X, You L, Liu H (2021) The expected values of Sombor indices in random hexagonal chains, phenylene chains and Sombor indices of some chemical graphs. Int J Quantum Chem 121:#e26740","journal-title":"Int J Quantum Chem"},{"key":"1852_CR10","first-page":"11","volume":"86","author":"I Gutman","year":"2021","unstructured":"Gutman I (2021) Geometric approach to degree-based topological indices: Sombor indices. MATCH Commun Math Comput Chem 86:11\u201316","journal-title":"MATCH Commun Math Comput Chem"},{"key":"1852_CR11","doi-asserted-by":"publisher","first-page":"1","DOI":"10.30538\/psrp-odam2021.0047","volume":"4","author":"I Gutman","year":"2021","unstructured":"Gutman I (2021) Some basic properties of Sombor indices. Open J Discret Appl Math 4:1\u20133","journal-title":"Open J Discret Appl Math"},{"key":"1852_CR12","first-page":"703","volume":"86","author":"B Horoldagva","year":"2021","unstructured":"Horoldagva B, Xu C (2021) On Sombor index of graphs. MATCH Commun Math Comput Chem 86:703\u2013713","journal-title":"MATCH Commun Math Comput Chem"},{"key":"1852_CR13","first-page":"#125855","volume":"395","author":"Y Jiang","year":"2021","unstructured":"Jiang Y, Lu M (2021) Maximal augmented Zagreb index of trees with given diameter. Appl Math Comput 395:#125855","journal-title":"Appl Math Comput"},{"key":"1852_CR14","doi-asserted-by":"publisher","first-page":"512","DOI":"10.1016\/j.dam.2020.01.035","volume":"283","author":"X Jiang","year":"2020","unstructured":"Jiang X, He W, Liu Q, Li J (2020) On the Kirchhoff index of bipartite graphs with given diameters. Discret Appl Math 283:512\u2013521","journal-title":"Discret Appl Math"},{"key":"1852_CR15","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1016\/j.laa.2021.02.023","volume":"620","author":"X Li","year":"2021","unstructured":"Li X, Wang Z (2021) Trees with extremal spectral radius of weighted adjacency matrices among trees weighted by degree-based indices. Linear Algebra Appl 620:61\u201375","journal-title":"Linear Algebra Appl"},{"key":"1852_CR16","first-page":"#126731","volume":"416","author":"S Li","year":"2022","unstructured":"Li S, Wang Z, Zhang M (2022) On the extremal Sombor index of trees with a given diameter. Appl Math Comput 416:#126731","journal-title":"Appl Math Comput"},{"key":"1852_CR17","doi-asserted-by":"crossref","unstructured":"Liu H, Chen H, Xiao Q, Fang X, Tang Z (2021) More on Sombor indices of chemical graphs and their applications to the boiling point of benzenoid hydrocarbons. Int J Quantum Chem 121:#e26689","DOI":"10.1002\/qua.26689"},{"key":"1852_CR18","first-page":"729","volume":"86","author":"H Liu","year":"2021","unstructured":"Liu H, You L, Tang Z, Liu JB (2021) On the reduced Sombor index and its applications. MATCH Commun Math Comput Chem 86:729\u2013753","journal-title":"MATCH Commun Math Comput Chem"},{"key":"1852_CR19","doi-asserted-by":"publisher","first-page":"5","DOI":"10.46793\/match.87-1.005L","volume":"87","author":"H Liu","year":"2022","unstructured":"Liu H, You L, Huang Y (2022) Ordering chemical graphs by Sombor indices and its applications. MATCH Commun Math Comput Chem 87:5\u201322","journal-title":"MATCH Commun Math Comput Chem"},{"key":"1852_CR20","doi-asserted-by":"publisher","first-page":"59","DOI":"10.46793\/match.87-1.059L","volume":"87","author":"H Liu","year":"2022","unstructured":"Liu H, You L, Huang Y, Fang X (2022) Spectral properties of p-Sombor matrices and beyond. MATCH Commun Math Comput Chem 87:59\u201387","journal-title":"MATCH Commun Math Comput Chem"},{"key":"1852_CR21","doi-asserted-by":"publisher","first-page":"445","DOI":"10.2298\/JSC201215006R","volume":"86","author":"I Red\u017eepovi\u0107","year":"2021","unstructured":"Red\u017eepovi\u0107 I (2021) Chemical applicability of Sombor indices. J Serb Chem Soc 86:445\u2013457","journal-title":"J Serb Chem Soc"},{"key":"1852_CR22","doi-asserted-by":"publisher","first-page":"438","DOI":"10.1016\/j.cam.2019.01.030","volume":"356","author":"Q Sun","year":"2019","unstructured":"Sun Q, Ikica B, \u0160krekovski R, Vuka\u0161inovi\u0107 V (2019) Graphs with a given diameter that maximise the Wiener index. Appl Math Comput 356:438\u2013448","journal-title":"Appl Math Comput"},{"key":"1852_CR23","first-page":"115","volume":"112","author":"L You","year":"2013","unstructured":"You L, Han H (2013) The maximum Sum-Balaban index of trees with given diameter. Ars Combin 112:115\u2013128","journal-title":"Ars Combin"},{"key":"1852_CR24","first-page":"#126521","volume":"411","author":"W Zhang","year":"2021","unstructured":"Zhang W, You L, Liu H, Huang Y (2021) The expected values and variances for Sombor indices in a general random chain. Appl Math Comput 411:#126521","journal-title":"Appl Math Comput"},{"key":"1852_CR25","doi-asserted-by":"publisher","first-page":"429","DOI":"10.7151\/dmgt.2007","volume":"38","author":"L Zhong","year":"2018","unstructured":"Zhong L (2018) The minimum harmonic index for unicyclic graphs with given diameter. Discuss Math Graph Theory 38:429\u2013442","journal-title":"Discuss Math Graph Theory"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01852-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-022-01852-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-022-01852-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,6,9]],"date-time":"2022-06-09T21:16:09Z","timestamp":1654809369000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-022-01852-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,13]]},"references-count":25,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2022,6]]}},"alternative-id":["1852"],"URL":"https:\/\/doi.org\/10.1007\/s40314-022-01852-z","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"value":"2238-3603","type":"print"},{"value":"1807-0302","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,13]]},"assertion":[{"value":"5 November 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 February 2022","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 March 2022","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"13 April 2022","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"138"}}