{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,29]],"date-time":"2026-01-29T16:30:12Z","timestamp":1769704212490,"version":"3.49.0"},"reference-count":26,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T00:00:00Z","timestamp":1769472000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Science Found of Qinghai Province","award":["2021-ZJ-703"],"award-info":[{"award-number":["2021-ZJ-703"]}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["12461065"],"award-info":[{"award-number":["12461065"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Science Foundation of China","doi-asserted-by":"crossref","award":["12261074"],"award-info":[{"award-number":["12261074"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A graph is planar if it can be embedded in the plane such that its edges intersect only at their common endpoints. In this paper, we determine the graphs attaining the second and third largest signless Laplacian spectral radii among all planar graphs of order n\u2265398. Furthermore, we apply this characterization to identify the planar graphs that achieve the first three largest values of the sum of the first and second largest signless Laplacian eigenvalues.<\/jats:p>","DOI":"10.3390\/axioms15020093","type":"journal-article","created":{"date-parts":[[2026,1,27]],"date-time":"2026-01-27T09:21:40Z","timestamp":1769505700000},"page":"93","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Ordering Planar Graphs by Their Signless Laplacian Spectral Radii"],"prefix":"10.3390","volume":"15","author":[{"given":"Ke","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhen","family":"Lin","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China"},{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Xining 810008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shumin","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China"},{"name":"The State Key Laboratory of Tibetan Intelligent Information Processing and Application, Qinghai Normal University, Xining 810008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chengfu","family":"Ye","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Qinghai Normal University, Xining 810008, China"},{"name":"Academy of Plateau Science and Sustainability, People\u2019s Government of Qinghai Province and Beijing Normal University, Xining 810008, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2026,1,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Barth\u00e9lemy, M. 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