{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T14:00:49Z","timestamp":1773669649008,"version":"3.50.1"},"reference-count":3,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":7611,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1985,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The <jats:italic>k<\/jats:italic>\u2010domination number of a graph <jats:italic>G<\/jats:italic>, \u03b3<jats:italic>k<\/jats:italic>(<jats:italic>G<\/jats:italic>), is the least cardinality of a set <jats:italic>U<\/jats:italic> of verticies such that any other vertex is adjacent to at least <jats:italic>k<\/jats:italic> vertices of <jats:italic>U.<\/jats:italic> We prove that if each vertex has degree at least <jats:italic>k<\/jats:italic>, then \u03b3<jats:italic>k<\/jats:italic>(<jats:italic>G<\/jats:italic>) \u2264 <jats:italic>kp<\/jats:italic>\/(<jats:italic>k<\/jats:italic> + 1).<\/jats:p>","DOI":"10.1002\/jgt.3190090414","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T11:48:23Z","timestamp":1180180103000},"page":"533-534","source":"Crossref","is-referenced-by-count":36,"title":["An upper bound for the <i>k<\/i>\u2010domination number of a graph"],"prefix":"10.1002","volume":"9","author":[{"given":"E. J.","family":"Cockayne","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Gamble","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"B.","family":"Shepherd","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"J. F.FinkandM. S.Jacobson On n\u2010domination n\u2010dependence and forbidden subgraphs. (Submitted.)"},{"key":"e_1_2_1_3_2","unstructured":"J. F.FinkandM. S.Jacobson n\u2010domination in graphs. (In preparation.)"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1090\/coll\/038"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190090414","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190090414","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T23:23:56Z","timestamp":1697757836000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190090414"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1985,12]]},"references-count":3,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1985,12]]}},"alternative-id":["10.1002\/jgt.3190090414"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190090414","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1985,12]]}}}