{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,29]],"date-time":"2026-08-29T05:46:43Z","timestamp":1787982403167,"version":"build-2784847793"},"reference-count":12,"publisher":"EDP Sciences","issue":"2","license":[{"start":{"date-parts":[[2024,3,27]],"date-time":"2024-03-27T00:00:00Z","timestamp":1711497600000},"content-version":"vor","delay-in-days":26,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003392","name":"Natural Science Foundation of Fujian Province","doi-asserted-by":"publisher","award":["2015J05017"],"award-info":[{"award-number":["2015J05017"]}],"id":[{"id":"10.13039\/501100003392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2024,2,5]]},"published-print":{"date-parts":[[2024,3]]},"abstract":"<jats:p>A set <jats:italic>S<\/jats:italic> of vertices in <jats:italic>G<\/jats:italic> is a semitotal dominating set of <jats:italic>G<\/jats:italic> if it is a dominating set of <jats:italic>G<\/jats:italic> and every vertex in <jats:italic>S<\/jats:italic> is within distance 2 of another vertex of <jats:italic>S<\/jats:italic>. The <jats:italic>semitotal domination number<\/jats:italic>, <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic>2<\/jats:sub>(<jats:italic>G<\/jats:italic>), is the minimum cardinality of a semitotal dominating set of <jats:italic>G<\/jats:italic>. Clearly, <jats:italic>\u03b3<\/jats:italic>(<jats:italic>G<\/jats:italic>) \u2264 <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic>2<\/jats:sub>(<jats:italic>G<\/jats:italic>) \u2264 <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>). In this paper, for any nontrivial tree <jats:italic>T<\/jats:italic> that is not a star, we investigate the ratios <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic>2<\/jats:sub>(<jats:italic>T<\/jats:italic> )\/<jats:italic>\u03b3<\/jats:italic>(<jats:italic>T<\/jats:italic>) and <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic> )\/<jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>t<\/jats:italic>2<\/jats:sub>(<jats:italic>T<\/jats:italic>), and provide constructive characterizations of trees achieving the upper bounds.<\/jats:p>","DOI":"10.1051\/ro\/2024037","type":"journal-article","created":{"date-parts":[[2024,2,8]],"date-time":"2024-02-08T20:00:30Z","timestamp":1707422430000},"page":"1249-1256","source":"Crossref","is-referenced-by-count":4,"title":["Semitotal domination <i>versus<\/i> domination and total domination in trees"],"prefix":"10.1051","volume":"58","author":[{"given":"Wei","family":"Zhuang","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2024,3,27]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1002\/jgt.3190030306","volume":"3","author":"Bollob\u00e1s","year":"1979","journal-title":"J. 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