{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T04:32:55Z","timestamp":1721709175460},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,6]]},"abstract":"<jats:p> Let \u03b3(D) denote the domination number of a digraph D and let C<jats:sub>m<\/jats:sub> \u2297 C<jats:sub>n<\/jats:sub> denote the strong product of C<jats:sub>m<\/jats:sub> and C<jats:sub>n<\/jats:sub>, the directed cycles of length m, n \u2265 2. In this paper, we determine the exact values [Formula: see text] Furthermore, we give a lower bound and an upper bound of \u03b3(C<jats:sub>m<jats:sub>1<\/jats:sub><\/jats:sub> \u2297 C<jats:sub>m<jats:sub>2<\/jats:sub><\/jats:sub> \u2297 \u22ef \u2297 C<jats:sub>m<jats:sub>n<\/jats:sub><\/jats:sub>) and obtain that [Formula: see text] when at least n-2 integers of {m<jats:sub>1<\/jats:sub>, m<jats:sub>2<\/jats:sub>, \u2026, m<jats:sub>n<\/jats:sub>} are even (because of the isomorphism, we assume that m<jats:sub>3<\/jats:sub>, m<jats:sub>4<\/jats:sub>, \u2026, m<jats:sub>n<\/jats:sub> are even). <\/jats:p>","DOI":"10.1142\/s1793830914500219","type":"journal-article","created":{"date-parts":[[2014,1,23]],"date-time":"2014-01-23T09:54:02Z","timestamp":1390470842000},"page":"1450021","source":"Crossref","is-referenced-by-count":2,"title":["THE DOMINATION NUMBER OF STRONG PRODUCT OF DIRECTED CYCLES"],"prefix":"10.1142","volume":"06","author":[{"given":"HUIPING","family":"CAI","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Sciences, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China"},{"name":"School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, P. R. China"}]},{"given":"JUAN","family":"LIU","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, P. R. China"}]},{"given":"LINGZHI","family":"QIAN","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences, Shihezi University, Shihezi, Xinjiang, 832003, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2014,3,19]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2007.03.027"},{"key":"rf2","volume-title":"Product Graphs: Structure and Recognition","author":"Imrich W.","year":"2000"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2009.11.005"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1007\/s10878-010-9314-x"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.7151\/dmgt.1668"},{"key":"rf7","first-page":"175","volume":"78","author":"Shaheen R. S.","journal-title":"Util. Math."},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/s00373-010-0919-8"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/S0898-1221(98)00169-2"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2010.10.001"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830914500219","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:44:22Z","timestamp":1565192662000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830914500219"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,19]]},"references-count":9,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2014,3,19]]},"published-print":{"date-parts":[[2014,6]]}},"alternative-id":["10.1142\/S1793830914500219"],"URL":"https:\/\/doi.org\/10.1142\/s1793830914500219","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,3,19]]}}}