{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T08:50:26Z","timestamp":1765183826519,"version":"3.46.0"},"reference-count":18,"publisher":"EDP Sciences","issue":"6","license":[{"start":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T00:00:00Z","timestamp":1765152000000},"content-version":"vor","delay-in-days":37,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12161085"],"award-info":[{"award-number":["12161085"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Xinjiang Key Laboratory of Applied Mathematics","award":["XJDX1401"],"award-info":[{"award-number":["XJDX1401"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2025,6,5]]},"published-print":{"date-parts":[[2025,11]]},"abstract":"<jats:p>\n                    The Sombor matrix\n                    <jats:italic>S<\/jats:italic>\n                    (\n                    <jats:italic>G<\/jats:italic>\n                    ) of a graph\n                    <jats:italic>G<\/jats:italic>\n                    was introduced by Gutman in 2021, in which the (\n                    <jats:italic>i, j<\/jats:italic>\n                    )-entry is equal to \u221a(deg\n                    <jats:sup>2<\/jats:sup>\n                    (\n                    <jats:italic>\n                      u\n                      <jats:sub>i<\/jats:sub>\n                    <\/jats:italic>\n                    ) + deg\n                    <jats:sup>2<\/jats:sup>\n                    (\n                    <jats:italic>\n                      u\n                      <jats:sub>j<\/jats:sub>\n                    <\/jats:italic>\n                    )) if the vertices\n                    <jats:italic>\n                      u\n                      <jats:sub>i<\/jats:sub>\n                    <\/jats:italic>\n                    and\n                    <jats:italic>\n                      u\n                      <jats:sub>j<\/jats:sub>\n                    <\/jats:italic>\n                    are adjacent in\n                    <jats:italic>G<\/jats:italic>\n                    , and zero otherwise, where deg(\n                    <jats:italic>\n                      u\n                      <jats:sub>i<\/jats:sub>\n                    <\/jats:italic>\n                    ) denotes the degree of vertex\n                    <jats:italic>\n                      u\n                      <jats:sub>i<\/jats:sub>\n                    <\/jats:italic>\n                    in\n                    <jats:italic>G<\/jats:italic>\n                    . In this paper, we obtain the extremal graphs with the first two maximum Sombor spectral radii in bicyclic graphs.\n                  <\/jats:p>","DOI":"10.1051\/ro\/2025075","type":"journal-article","created":{"date-parts":[[2025,6,11]],"date-time":"2025-06-11T03:45:02Z","timestamp":1749613502000},"page":"3549-3562","source":"Crossref","is-referenced-by-count":0,"title":["The first two maximum Sombor spectral radii of bicyclic graphs"],"prefix":"10.1051","volume":"59","author":[{"given":"Yanhui","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi","place":["P.R. China"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoling","family":"Ma","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi","place":["P.R. 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