{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:23:01Z","timestamp":1759638181538},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","funder":[{"name":"Tata Realty Infrastructure Limited"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:p> For a graph [Formula: see text] with vertex set [Formula: see text] and edge set [Formula: see text], a subset [Formula: see text] of [Formula: see text] is the total edge dominating set if every edge in [Formula: see text] is adjacent to at least one edge in [Formula: see text]. The minimum cardinality of a total edge dominated set, denoted by [Formula: see text], is called the total edge domination number of a graph [Formula: see text]. We prove that for every tree [Formula: see text] of diameter at least two with [Formula: see text] leaves and [Formula: see text] support vertices we have [Formula: see text], and we characterize the trees attaining each of the bounds. <\/jats:p>","DOI":"10.1142\/s1793830921500117","type":"journal-article","created":{"date-parts":[[2020,8,29]],"date-time":"2020-08-29T08:41:22Z","timestamp":1598690482000},"page":"2150011","source":"Crossref","is-referenced-by-count":1,"title":["Bounds on total edge domination number of a tree"],"prefix":"10.1142","volume":"13","author":[{"given":"B.","family":"Senthilkumar","sequence":"first","affiliation":[{"name":"Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamilnadu 613401, India"}]},{"given":"H.","family":"Naresh Kumar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamilnadu 613401, India"}]},{"given":"Y. B.","family":"Venkatakrishnan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, SASTRA Deemed University, Thanjavur, Tamilnadu 613401, India"}]}],"member":"219","published-online":{"date-parts":[[2020,9,25]]},"reference":[{"key":"S1793830921500117BIB001","first-page":"189","volume":"58","author":"Chellali M.","year":"2006","journal-title":"J. Comb. Math. Comb. Comput."},{"key":"S1793830921500117BIB002","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.crma.2014.03.017","volume":"352","author":"Krishnakumari B.","year":"2014","journal-title":"Comptes Rendus Math."},{"key":"S1793830921500117BIB003","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/j.crma.2010.11.021","volume":"349","author":"Krzywkowski M.","year":"2011","journal-title":"Comptes Rendus Math."},{"key":"S1793830921500117BIB004","series-title":"Centre Mathematics Science","first-page":"75","volume-title":"Proc. Symp. Graph Theory and Combinatorics","volume":"21","author":"Kulli V. R.","year":"1991"},{"key":"S1793830921500117BIB005","doi-asserted-by":"crossref","first-page":"165","DOI":"10.7151\/dmgt.1222","volume":"24","author":"Lema\u0144ska M.","year":"2004","journal-title":"Discuss. Math. Graph Theory"},{"key":"S1793830921500117BIB006","first-page":"489","volume":"19","author":"Mitchell S.","year":"1977","journal-title":"Congr. Numer."},{"key":"S1793830921500117BIB007","first-page":"1077","volume":"10","author":"Paspasan M. N. S.","year":"2016","journal-title":"Appl. Math. Sci."},{"key":"S1793830921500117BIB008","doi-asserted-by":"crossref","first-page":"571","DOI":"10.1007\/s10878-020-00596-y","volume":"40","author":"Pan Z.","year":"2020","journal-title":"J. Combin. Optim."},{"key":"S1793830921500117BIB009","first-page":"198","volume":"5","author":"Velammal S.","year":"2014","journal-title":"Int. J. Enhanced Res. Sci. Technol. Eng."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830921500117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,2,8]],"date-time":"2021-02-08T16:56:46Z","timestamp":1612803406000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830921500117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,9,25]]},"references-count":9,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["10.1142\/S1793830921500117"],"URL":"https:\/\/doi.org\/10.1142\/s1793830921500117","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,9,25]]}}}