{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:30Z","timestamp":1740155970807,"version":"3.37.3"},"reference-count":6,"publisher":"World Scientific Pub Co Pte Ltd","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,10]]},"abstract":"<jats:p> Let [Formula: see text] be a simple and connected graph. A dominating set [Formula: see text] is said to be a vertex covering transversal dominating set if it intersects every minimum vertex covering set of [Formula: see text]. The vertex covering transversal domination number [Formula: see text] is the minimum cardinality among all vertex covering transversal dominating sets of [Formula: see text]. A vertex covering transversal dominating set of minimum cardinality [Formula: see text] is called a minimum vertex covering transversal dominating set or simply a [Formula: see text]-set. In this paper, we prove some general theorems on the vertex covering transversal domination number of a simple connected graph. We also provide some results about [Formula: see text]-sets and try to classify those sets based on their intersection with the minimum vertex covering sets. <\/jats:p>","DOI":"10.1142\/s1793830917500690","type":"journal-article","created":{"date-parts":[[2017,9,28]],"date-time":"2017-09-28T00:13:08Z","timestamp":1506557588000},"page":"1750069","source":"Crossref","is-referenced-by-count":2,"title":["On the minimum vertex covering transversal dominating sets in graphs and their classification"],"prefix":"10.1142","volume":"09","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6453-320X","authenticated-orcid":false,"given":"R.","family":"Vasanthi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Alagappa Chettiar College of Engineering and Technology, Karaikudi, Tamilnadu, India"}]},{"given":"K.","family":"Subramanian","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Alagappa Government Arts College, Karaikudi, Tamilnadu, India"}]}],"member":"219","published-online":{"date-parts":[[2017,11,2]]},"reference":[{"key":"S1793830917500690BIB002","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230070305"},{"key":"S1793830917500690BIB003","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1581"},{"volume-title":"Theory of Domination in Graphs","year":"2010","author":"Kulli V. R.","key":"S1793830917500690BIB004"},{"issue":"2","key":"S1793830917500690BIB005","doi-asserted-by":"crossref","first-page":"01","DOI":"10.26708\/IJMSC.2015.2.5.01","volume":"5","author":"Vasanthi R.","year":"2015","journal-title":"Int. J. Math. Soft Comput."},{"key":"S1793830917500690BIB006","doi-asserted-by":"publisher","DOI":"10.1155\/2016\/1029024"},{"volume-title":"Introduction to Graph Theory","year":"2001","author":"West D. B.","key":"S1793830917500690BIB007"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830917500690","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:24:55Z","timestamp":1565141095000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500690"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,10]]},"references-count":6,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2017,11,2]]},"published-print":{"date-parts":[[2017,10]]}},"alternative-id":["10.1142\/S1793830917500690"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500690","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2017,10]]}}}