{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,7,15]],"date-time":"2023-07-15T04:15:32Z","timestamp":1689394532727},"reference-count":15,"publisher":"EDP Sciences","issue":"4","license":[{"start":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T00:00:00Z","timestamp":1689292800000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"name":"Department of Science and Technology, India","award":["MTR\/2018\/000234"],"award-info":[{"award-number":["MTR\/2018\/000234"]}]},{"name":"TATA Realty Infrastructure Limited"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["RAIRO-Oper. Res."],"accepted":{"date-parts":[[2023,5,30]]},"published-print":{"date-parts":[[2023,7]]},"abstract":"<jats:p>A vertex <jats:italic>u<\/jats:italic> of a graph <jats:italic>G<\/jats:italic> = (<jats:italic>V<\/jats:italic>,\u00a0<jats:italic>E<\/jats:italic>), <jats:italic>ve<\/jats:italic>-dominates every edge incident to <jats:italic>u<\/jats:italic>, as well as every edge adjacent to these incident edges. A set <jats:italic>S<\/jats:italic> \u2286\u00a0<jats:italic>V<\/jats:italic> is a vertex-edge dominating set (or a <jats:italic>ved-set<\/jats:italic> for short) if every edge of <jats:italic>E<\/jats:italic> is <jats:italic>ve-<\/jats:italic>dominated by at least one vertex of <jats:italic>S<\/jats:italic>. The vertex-edge domination number is the minimum cardinality of a <jats:italic>ved-set<\/jats:italic> in <jats:italic>G<\/jats:italic>. In this paper, we investigate the graphs having unique minimum <jats:italic>ved-sets<\/jats:italic> that we will call UVED-graphs. We start by giving some basic properties of UVED-graphs. For the class of trees, we establish two equivalent conditions characterizing UVED-trees which we subsequently complete by providing a constructive characterization.<\/jats:p>","DOI":"10.1051\/ro\/2023074","type":"journal-article","created":{"date-parts":[[2023,5,31]],"date-time":"2023-05-31T19:06:03Z","timestamp":1685559963000},"page":"1785-1795","source":"Crossref","is-referenced-by-count":0,"title":["Graphs with unique minimum vertex-edge dominating sets"],"prefix":"10.1051","volume":"57","author":[{"given":"B.","family":"Senthilkumar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"M.","family":"Chellali","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"H.","family":"Naresh Kumar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yanamandram B.","family":"Venkatakrishnan","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2023,7,14]]},"reference":[{"key":"R1","first-page":"225","volume":"76","author":"Blidia","year":"2011","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"R2","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s00010-015-0354-2","volume":"90","author":"Boutrig","year":"2016","journal-title":"Aequat. Math."},{"key":"R3","first-page":"3","volume":"73","author":"Chellali","year":"2004","journal-title":"Ars Combin."},{"key":"R4","first-page":"233","volume":"83","author":"Chellali","year":"2010","journal-title":"Util. Math."},{"key":"R5","first-page":"177","volume":"119","author":"Chen","year":"2015","journal-title":"Ars Combin."},{"key":"R6","doi-asserted-by":"crossref","first-page":"247","DOI":"10.1016\/S0012-365X(01)00196-0","volume":"240","author":"Fischermann","year":"2001","journal-title":"Discrete Math."},{"key":"R7","first-page":"117","volume":"25","author":"Fischermann","year":"2002","journal-title":"Aust. J. Combin."},{"key":"R8","first-page":"55","volume":"101","author":"Gunther","year":"1994","journal-title":"Congr. Numer."},{"key":"R9","doi-asserted-by":"crossref","first-page":"233","DOI":"10.7151\/dmgt.1172","volume":"22","author":"Haynes","year":"2002","journal-title":"Discuss. Math. Graph Theory"},{"key":"R10","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.crma.2014.03.017","volume":"352","author":"Krishnakumari","year":"2014","journal-title":"C. R. Math."},{"key":"R11","unstructured":"Lewis J.R., Vertex-edge and edge-vertex domination in graphs. Ph.D. Thesis, Clemson University, Clemson (2007)."},{"key":"R12","first-page":"193","volume":"81","author":"Lewis","year":"2010","journal-title":"Util. Math."},{"key":"R13","unstructured":"Peters J.W., Theoretical and algorithmic results on domination and connectivity. Ph.D. thesis, Clemson University, Clemson, SC (1986)."},{"key":"R14","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1080\/23799927.2018.1531930","volume":"3","author":"Zaho","year":"2018","journal-title":"Int. J. Comput. Math. Comput. Syst. Theory"},{"key":"R15","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/s00010-018-0609-9","volume":"93","author":"\u017byli\u0144ski","year":"2019","journal-title":"Aequat. Math."}],"container-title":["RAIRO - Operations Research"],"original-title":[],"link":[{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023074\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,7,14]],"date-time":"2023-07-14T08:30:45Z","timestamp":1689323445000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.rairo-ro.org\/10.1051\/ro\/2023074"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,7]]},"references-count":15,"journal-issue":{"issue":"4"},"alternative-id":["ro220253"],"URL":"https:\/\/doi.org\/10.1051\/ro\/2023074","relation":{},"ISSN":["0399-0559","2804-7303"],"issn-type":[{"value":"0399-0559","type":"print"},{"value":"2804-7303","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,7]]}}}