{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T13:26:59Z","timestamp":1777382819045,"version":"3.51.4"},"reference-count":28,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2024,2,28]],"date-time":"2024-02-28T00:00:00Z","timestamp":1709078400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai Municipality","doi-asserted-by":"publisher","award":["22ZR1416300"],"award-info":[{"award-number":["22ZR1416300"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007219","name":"Natural Science Foundation of Shanghai Municipality","doi-asserted-by":"publisher","award":["23JC1401500"],"award-info":[{"award-number":["23JC1401500"]}],"id":[{"id":"10.13039\/100007219","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271162"],"award-info":[{"award-number":["12271162"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12161141006"],"award-info":[{"award-number":["12161141006"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12326372"],"award-info":[{"award-number":["12326372"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[2024,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Given a planar graph family , let  and  be the maximum size and maximum spectral radius over all \u2010vertex \u2010free planar graphs, respectively. Let  be the disjoint union of  copies of \u2010cycles, and  be the family of  vertex\u2010disjoint cycles without length restriction. Tait and Tobin determined that  is the extremal spectral graph among all planar graphs with sufficiently large order , which implies the extremal graphs of both  and  for  are . In this paper, we first determine  and  and characterize the unique extremal graph for ,  and sufficiently large . Second, we obtain the exact values of  and , which solve a conjecture of Li for .<\/jats:p>","DOI":"10.1002\/jgt.23084","type":"journal-article","created":{"date-parts":[[2024,2,29]],"date-time":"2024-02-29T07:58:45Z","timestamp":1709193525000},"page":"496-524","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Extremal spectral results of planar graphs without vertex\u2010disjoint cycles"],"prefix":"10.1002","volume":"106","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-1957-3949","authenticated-orcid":false,"given":"Longfei","family":"Fang","sequence":"first","affiliation":[{"name":"School of Mathematics East China University of Science and Technology Shanghai China"},{"name":"School of Mathematics and Finance Chuzhou University Chuzhou Anhui China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6072-4647","authenticated-orcid":false,"given":"Huiqiu","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematics East China University of Science and Technology Shanghai China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9406-7967","authenticated-orcid":false,"given":"Yongtang","family":"Shi","sequence":"additional","affiliation":[{"name":"Center for Combinatorics and LPMC Nankai University Tianjin China"}]}],"member":"311","published-online":{"date-parts":[[2024,2,28]]},"reference":[{"key":"e_1_2_8_2_1","doi-asserted-by":"crossref","unstructured":"J. A.BondyandU. S. R.Murty Graph theory Springer\u2010Verlag Berlin 2008.","DOI":"10.1007\/978-1-84628-970-5"},{"key":"e_1_2_8_3_1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1538-4632.1991.tb00239.x"},{"key":"e_1_2_8_4_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(93)90139-F"},{"key":"e_1_2_8_5_1","doi-asserted-by":"publisher","DOI":"10.37236\/10774"},{"key":"e_1_2_8_6_1","unstructured":"S.Cioab\u0103 D. N.Desai andM.Tait The spectral even cycle problem arxiv:2205.00990v1 2022."},{"key":"e_1_2_8_7_1","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.21991"},{"key":"e_1_2_8_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s41980-021-00644-1"},{"key":"e_1_2_8_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01650069"},{"key":"e_1_2_8_10_1","doi-asserted-by":"publisher","DOI":"10.5486\/PMD.1962.9.1-2.02"},{"key":"e_1_2_8_11_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2021.112794"},{"key":"e_1_2_8_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2023.113655"},{"key":"e_1_2_8_13_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0963548314000601"},{"key":"e_1_2_8_14_1","first-page":"167","article-title":"The history of degenerate (bipartite) extremal graph problems","volume":"25","author":"F\u00fcredi Z.","year":"2013","journal-title":"Bolyai Soc. Stud. (Erd\u0151s Centennial)"},{"key":"e_1_2_8_15_1","doi-asserted-by":"publisher","DOI":"10.1137\/21M140657X"},{"key":"e_1_2_8_16_1","unstructured":"E.Gy\u0151ri A.Li andR. T.Zhou The planar Tur\u00e1n number of the seven\u2010cycle arxiv:2307.06909v2."},{"key":"e_1_2_8_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2019.111610"},{"key":"e_1_2_8_18_1","doi-asserted-by":"publisher","DOI":"10.37236\/8255"},{"key":"e_1_2_8_19_1","first-page":"200","article-title":"Planar Tur\u00e1n number and planar anti\u2010Ramsey number of graphs","volume":"25","author":"Lan Y. X.","year":"2021","journal-title":"Oper. Res. Trans"},{"key":"e_1_2_8_20_1","unstructured":"Y. X.Lan Y. T.Shi andZ.\u2010X.Song Planar Tur\u00e1n number of cubic graphs and disjoint union of cycles arxiv:2202.09216v2 2022."},{"key":"e_1_2_8_21_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2023.09.021"},{"key":"e_1_2_8_22_1","doi-asserted-by":"publisher","DOI":"10.4153\/CJM-1968-012-x"},{"key":"e_1_2_8_23_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.09.029"},{"key":"e_1_2_8_24_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2007.07.010"},{"key":"e_1_2_8_25_1","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1996.0036"},{"key":"e_1_2_8_26_1","unstructured":"R. L.Shi Z.Walsh andX. X.Yu Planar Tur\u00e1n number of the 7\u2010cycle arxiv:2306.13594v1."},{"key":"e_1_2_8_27_1","unstructured":"R. L.Shi Z.Walsh andX. X.Yu Dense circuit graphs and the planar Tur\u00e1n number of a cycle arxiv:2310.06631v1."},{"key":"e_1_2_8_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jctb.2017.04.006"},{"key":"e_1_2_8_29_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.laa.2012.05.006"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.23084","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,5,13]],"date-time":"2024-05-13T14:49:36Z","timestamp":1715611776000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.23084"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,2,28]]},"references-count":28,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2024,7]]}},"alternative-id":["10.1002\/jgt.23084"],"URL":"https:\/\/doi.org\/10.1002\/jgt.23084","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,2,28]]},"assertion":[{"value":"2023-02-27","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-01-23","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-02-28","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}