{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T09:05:44Z","timestamp":1777539944403,"version":"3.51.4"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2016,12]]},"abstract":"<jats:p> A vertex of a graph [Formula: see text] is said to dominate itself and all its neighbors. A double dominating set (DDS) of a graph [Formula: see text] is a set [Formula: see text] of vertices such that every vertex of [Formula: see text] is dominated by at least two vertices of [Formula: see text]. The double domination number of a graph [Formula: see text] is the minimum cardinality of a DDS of [Formula: see text]. For a graph [Formula: see text], a subset [Formula: see text] of [Formula: see text] is a super dominating set SDS if for every vertex of [Formula: see text] there exists an external private neighbor of [Formula: see text] with respect to [Formula: see text]. The super domination number of [Formula: see text] is the minimum cardinality of a SDS of [Formula: see text]. We prove that for every tree [Formula: see text], [Formula: see text], and we characterize the trees attaining this bound. <\/jats:p>","DOI":"10.1142\/s1793830916500671","type":"journal-article","created":{"date-parts":[[2016,9,9]],"date-time":"2016-09-09T06:15:41Z","timestamp":1473401741000},"page":"1650067","source":"Crossref","is-referenced-by-count":12,"title":["Double domination and super domination in trees"],"prefix":"10.1142","volume":"08","author":[{"given":"B.","family":"Krishnakumari","sequence":"first","affiliation":[{"name":"Department of Mathematics, SASTRA University Tanjore, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Y. B.","family":"Venkatakrishnan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, SASTRA University Tanjore, Tamilnadu, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,11,8]]},"reference":[{"key":"S1793830916500671BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.dam.2007.03.007"},{"key":"S1793830916500671BIB002","first-page":"157","volume":"47","author":"Chellali M.","year":"2010","journal-title":"Australas. J. Combin."},{"key":"S1793830916500671BIB003","first-page":"451","volume":"25","author":"Chen X.","year":"2005","journal-title":"J. Math. Res. Exposition"},{"key":"S1793830916500671BIB004","first-page":"131","volume":"91","author":"Desormeaux J. W.","year":"2013","journal-title":"Util. Math."},{"key":"S1793830916500671BIB005","first-page":"11","volume":"76","author":"Harant J.","year":"2008","journal-title":"Util. Math."},{"key":"S1793830916500671BIB006","first-page":"201","volume":"55","author":"Harary F.","year":"2000","journal-title":"Ars Combin."},{"key":"S1793830916500671BIB007","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T.","year":"1998"},{"key":"S1793830916500671BIB008","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T.","year":"1998"},{"key":"S1793830916500671BIB009","first-page":"3","volume":"102","author":"Krzywkowski M.","year":"2011","journal-title":"Ars Combin."},{"key":"S1793830916500671BIB010","first-page":"427","volume":"39","author":"Krzywkowski M.","year":"2013","journal-title":"Houston J. Math."},{"key":"S1793830916500671BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s40010-015-0208-2"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830916500671","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T18:08:46Z","timestamp":1565201326000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830916500671"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,11,8]]},"references-count":11,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2016,11,8]]},"published-print":{"date-parts":[[2016,12]]}},"alternative-id":["10.1142\/S1793830916500671"],"URL":"https:\/\/doi.org\/10.1142\/s1793830916500671","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,11,8]]}}}