{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:32:26Z","timestamp":1740133946887,"version":"3.37.3"},"reference-count":9,"publisher":"World Scientific Pub Co Pte Ltd","issue":"07","funder":[{"DOI":"10.13039\/501100001843","name":"Science and Engineering Research Board","doi-asserted-by":"crossref","award":["MTR\/2018\/000234"],"award-info":[{"award-number":["MTR\/2018\/000234"]}],"id":[{"id":"10.13039\/501100001843","id-type":"DOI","asserted-by":"crossref"}]},{"name":"TATA Realty Infrastructure Limited"},{"DOI":"10.13039\/501100009536","name":"SASTRA University","doi-asserted-by":"crossref","award":["SR\/FST\/MSI-107\/2015(c)"],"award-info":[{"award-number":["SR\/FST\/MSI-107\/2015(c)"]}],"id":[{"id":"10.13039\/501100009536","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2024,11]]},"abstract":"<jats:p> A vertex [Formula: see text] of a simple graph [Formula: see text] ve-dominates every edge incident to [Formula: see text] as well as every edge adjacent to these incident edges. A set [Formula: see text] is a total vertex-edge dominating set if every edge of [Formula: see text] is ve-dominated by a vertex of [Formula: see text] and the subgraph induced by [Formula: see text] has no isolated vertex. The total vertex-edge domination problem is to find a total vertex-edge dominating set of minimum cardinality. In this paper, we first show that the total vertex-edge domination problem is NP-complete for chordal graphs. Then we provide a linear-time algorithm for this problem in trees. Moreover, we show that the minimum total vertex-edge domination problem cannot be approximated within [Formula: see text] for any [Formula: see text] unless [Formula: see text]). Finally, we prove that the minimum total vertex-edge domination problem is APX-complete for bounded-degree graphs. <\/jats:p>","DOI":"10.1142\/s0129054123500247","type":"journal-article","created":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T13:52:46Z","timestamp":1697723566000},"page":"857-869","source":"Crossref","is-referenced-by-count":0,"title":["Algorithmic Aspects of Total Vertex-Edge Domination in Graphs"],"prefix":"10.1142","volume":"35","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1717-239X","authenticated-orcid":false,"given":"H. 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B.","family":"Venkatakrishnan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Arts, Science, Humanities and Education, SASTRA Deemed University, Thanjavur, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2023,10,19]]},"reference":[{"key":"S0129054123500247BIB001","doi-asserted-by":"publisher","DOI":"10.1080\/00207160.2017.1343469"},{"key":"S0129054123500247BIB002","doi-asserted-by":"publisher","DOI":"10.1007\/s00010-015-0354-2"},{"key":"S0129054123500247BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/j.tcs.2018.09.019"},{"key":"S0129054123500247BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-6525-6"},{"key":"S0129054123500247BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2014.03.017"},{"key":"S0129054123500247BIB007","first-page":"193","volume":"81","author":"Lewis J. 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