{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T13:27:47Z","timestamp":1740144467136,"version":"3.37.3"},"reference-count":7,"publisher":"EDP Sciences","issue":"3","license":[{"start":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T00:00:00Z","timestamp":1687305600000},"content-version":"vor","delay-in-days":51,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,6,7]]},"published-print":{"date-parts":[[2023,5]]},"abstract":"<jats:p>An edge in a graph <jats:italic>G<\/jats:italic> = (<jats:italic>V<\/jats:italic>, <jats:italic>E<\/jats:italic>) is said to <jats:italic>ev<\/jats:italic>-dominate the vertices incident to it as well as the vertices adjacent to these incident vertices. A subset <jats:italic>F<\/jats:italic> \u2286 <jats:italic>E<\/jats:italic> is an edge-vertex dominating set (or simply, <jats:italic>ev<\/jats:italic>-dominating set) if every vertex is <jats:italic>ev<\/jats:italic>-dominated by at least one edge of <jats:italic>F<\/jats:italic>. The <jats:italic>ev<\/jats:italic>-domination number <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) is the minimum cardinality of a <jats:italic>ev<\/jats:italic>-dominating set of <jats:italic>G<\/jats:italic>. An <jats:italic>ev<\/jats:italic>-dominating set is independent if its edges are independent. The independent <jats:italic>ev<\/jats:italic>-domination number <jats:italic>i<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) is the minimum cardinality of an independent <jats:italic>ev<\/jats:italic>-dominating set and the upper independent <jats:italic>ev<\/jats:italic>-domination number <jats:italic>\u03b2<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>G<\/jats:italic>) is the maximum cardinality of a minimal independent <jats:italic>ev<\/jats:italic>-dominating set of <jats:italic>G<\/jats:italic>. In this paper, we show that for every nontrivial tree <jats:italic>T<\/jats:italic>, <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>) = <jats:italic>i<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>) \u2264 <jats:italic>\u03b3<\/jats:italic>(<jats:italic>T<\/jats:italic>)\u00a0\u2264\u00a0<jats:italic>\u03b2<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>), where <jats:italic>\u03b3<\/jats:italic>(<jats:italic>T<\/jats:italic>) is the domination number of <jats:italic>T<\/jats:italic>. Moreover, we provide a characterization of all trees <jats:italic>T<\/jats:italic> with <jats:italic>i<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>) = <jats:italic>\u03b2<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>), which we call well <jats:italic>ev<\/jats:italic>-covered trees, as well as a characterization of all trees <jats:italic>T<\/jats:italic> with <jats:italic>\u03b3<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>) = <jats:italic>i<\/jats:italic><jats:sub><jats:italic>ev<\/jats:italic><\/jats:sub>(<jats:italic>T<\/jats:italic>) = <jats:italic>\u03b3<\/jats:italic>(<jats:italic>T<\/jats:italic>).<\/jats:p>","DOI":"10.1051\/ro\/2023088","type":"journal-article","created":{"date-parts":[[2023,6,8]],"date-time":"2023-06-08T19:06:00Z","timestamp":1686251160000},"page":"1481-1489","source":"Crossref","is-referenced-by-count":1,"title":["Well <i>ev<\/i>-covered trees"],"prefix":"10.1051","volume":"57","author":[{"given":"Razika","family":"Boutrig","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5231-6195","authenticated-orcid":false,"given":"Mustapha","family":"Chellali","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2023,6,21]]},"reference":[{"key":"R1","first-page":"3","volume":"71","author":"Haynes","year":"2006","journal-title":"Util. Math."},{"key":"R2","first-page":"1","volume":"LXVI","author":"Hedetniemi","year":"2014","journal-title":"Graph Theory Notes New York"},{"key":"R3","first-page":"187","volume":"74","author":"Henning","year":"2007","journal-title":"Util. Math."},{"key":"R4","unstructured":"Lewis J.R., Vertex-edge and edge-vertex domination in graphs. Ph.D. thesis, Clemson University (2007)."},{"key":"R5","unstructured":"Peters J.W., Theoretical and algorithmic results on domination and connectivity. Ph.D. thesis, Clemson University (1986)."},{"key":"R6","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0021-9800(70)80011-4","volume":"8","author":"Plummer","year":"1970","journal-title":"J. Combin. Theory"},{"key":"R7","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1080\/16073606.1993.9631737","volume":"16","author":"Plummer","year":"1993","journal-title":"Quaest. Math."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023088\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,21]],"date-time":"2023-06-21T08:14:44Z","timestamp":1687335284000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023088"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,5]]},"references-count":7,"journal-issue":{"issue":"3"},"alternative-id":["ro220517"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2023088","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"type":"print","value":"0399-0559"},{"type":"electronic","value":"2804-7303"}],"subject":[],"published":{"date-parts":[[2023,5]]}}}