{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,29]],"date-time":"2025-10-29T03:49:19Z","timestamp":1761709759925},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","funder":[{"name":"MATRICS, DST-SERB","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":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,2]]},"abstract":"<jats:p> A vertex [Formula: see text] of a graph [Formula: see text] is said to vertex-edge dominate every edge incident to [Formula: see text], as well as every edge adjacent to these incident edges. A subset [Formula: see text] is a vertex-edge dominating set (ve-dominating set) if every edge of [Formula: see text] is vertex-edge dominated by at least one vertex of [Formula: see text]. A vertex-edge dominating set is said to be total if its induced subgraph has no isolated vertices. The minimum cardinality of a total vertex-edge dominating set of [Formula: see text], denoted by [Formula: see text], is called the total vertex-edge domination number of [Formula: see text]. In this paper, we prove that for every nontrivial tree of order [Formula: see text], with [Formula: see text] leaves and [Formula: see text] support vertices we have [Formula: see text], and we characterize extremal trees attaining the lower bound. <\/jats:p>","DOI":"10.1142\/s1793830920500913","type":"journal-article","created":{"date-parts":[[2020,7,15]],"date-time":"2020-07-15T02:34:02Z","timestamp":1594780442000},"page":"2050091","source":"Crossref","is-referenced-by-count":3,"title":["A lower bound on the total vertex-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":[[2020,8,18]]},"reference":[{"issue":"9","key":"S1793830920500913BIB001","doi-asserted-by":"crossref","first-page":"1820","DOI":"10.1080\/00207160.2017.1343469","volume":"95","author":"Bourtig R.","year":"2018","journal-title":"Int. J. Comput. Math."},{"key":"S1793830920500913BIB002","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1007\/s00010-015-0354-2","volume":"90","author":"Boutrig R.","year":"2016","journal-title":"Aequat. Math."},{"key":"S1793830920500913BIB003","first-page":"189","volume":"58","author":"Chellali M.","year":"2006","journal-title":"J. Combin. Math. Combin. Comput."},{"key":"S1793830920500913BIB004","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T.","year":"1998"},{"key":"S1793830920500913BIB005","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T.","year":"1998"},{"key":"S1793830920500913BIB006","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 Mathematique"},{"key":"S1793830920500913BIB008","first-page":"193","volume":"81","author":"Lewis J.","year":"2010","journal-title":"Utilitas Mathematica"},{"key":"S1793830920500913BIB009","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/s00010-018-0609-9","volume":"93","author":"Pawel \u0179.","year":"2019","journal-title":"Aequat. Math."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830920500913","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T10:59:16Z","timestamp":1611053956000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500913"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,18]]},"references-count":8,"journal-issue":{"issue":"01","published-print":{"date-parts":[[2021,2]]}},"alternative-id":["10.1142\/S1793830920500913"],"URL":"https:\/\/doi.org\/10.1142\/s1793830920500913","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,8,18]]}}}