{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:53:35Z","timestamp":1760147615592,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T00:00:00Z","timestamp":1676419200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100015310","name":"Natural Science Foundation of Xinjiang","doi-asserted-by":"publisher","award":["2020D04046"],"award-info":[{"award-number":["2020D04046"]}],"id":[{"id":"10.13039\/501100015310","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we present the upper and lower bounds on Sombor index SO(G) among all connected graphs (respectively, connected bipartite graphs). We give some sharp lower and upper bounds on SO(G) among connected graphs in terms of some parameters, including chromatic, girth and matching number. Meanwhile, we characterize the extremal graphs attaining those bounds. In addition, we give upper bounds on SO(G) among connected bipartite graphs with given matching number and\/or connectivity and determine the corresponding extremal connected bipartite graphs.<\/jats:p>","DOI":"10.3390\/axioms12020203","type":"journal-article","created":{"date-parts":[[2023,2,15]],"date-time":"2023-02-15T01:38:18Z","timestamp":1676425098000},"page":"203","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Extremal Graphs for Sombor Index with Given Parameters"],"prefix":"10.3390","volume":"12","author":[{"given":"Wanping","family":"Zhang","sequence":"first","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jixiang","family":"Meng","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Na","family":"Wang","sequence":"additional","affiliation":[{"name":"College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,15]]},"reference":[{"key":"ref_1","first-page":"11","article-title":"Geometric approach to degree-based topological indices: Sombor indices","volume":"86","author":"Gutman","year":"2021","journal-title":"MATCH Commun. 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