{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T11:13:16Z","timestamp":1769166796606,"version":"3.49.0"},"reference-count":19,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:p> In this paper, a new definition of graph domination called \u201cCaptive Domination\u201d is introduced. The proper subset of the vertices of a graph [Formula: see text] is a captive dominating set if it is a total dominating set and each vertex in this set dominates at least one vertex which doesn\u2019t belong to the dominating set. The inverse captive domination is also introduced. The lower and upper bounds for the number of edges of the graph are presented by using the captive domination number. Moreover, the lower and upper bounds for the captive domination number are found by using the number of vertices. The condition when the total domination and captive domination number are equal to two is discussed and obtained results. The captive domination in complement graphs is discussed. Finally, the captive dominating set of paths and cycles are determined. <\/jats:p>","DOI":"10.1142\/s1793830920500767","type":"journal-article","created":{"date-parts":[[2020,6,6]],"date-time":"2020-06-06T14:34:56Z","timestamp":1591454096000},"page":"2050076","source":"Crossref","is-referenced-by-count":25,"title":["Captive domination in graphs"],"prefix":"10.1142","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1125-4439","authenticated-orcid":false,"given":"Manal N.","family":"Al-Harere","sequence":"first","affiliation":[{"name":"Department of Applied Sciences, University of Technology, Baghdad, Iraq"}]},{"given":"Ahmed A.","family":"Omran","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education for Pure Science, University of Babylon, Babylon, Iraq"}]},{"given":"Athraa T.","family":"Breesam","sequence":"additional","affiliation":[{"name":"Department of Applied Sciences, University of Technology, Baghdad, Iraq"}]}],"member":"219","published-online":{"date-parts":[[2020,7,17]]},"reference":[{"issue":"2","key":"S1793830920500767BIB001","first-page":"51","author":"Abdlhusein M. 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