{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:34Z","timestamp":1753893814676,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>In this note we prove the following conjecture of Nowakowski and Rall: For arbitrary graphs $G$ and $H$ the upper domination number of the Cartesian product $G \\,\\square \\, H$ is at least the product of their upper domination numbers, in symbols: $\\Gamma(G \\,\\square \\, H)\\ge \\Gamma(G)\\Gamma(H).$<\/jats:p>","DOI":"10.37236\/1979","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:11:18Z","timestamp":1578719478000},"source":"Crossref","is-referenced-by-count":7,"title":["Vizing-like Conjecture for the Upper Domination of Cartesian Products of Graphs &amp;ndash; The Proof"],"prefix":"10.37236","volume":"12","author":[{"given":"Bo\u0161tjan","family":"Bre\u0161ar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2005,7,19]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v12i1n12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:48:17Z","timestamp":1579322897000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v12i1n12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,7,19]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2005,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1979","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2005,7,19]]},"article-number":"N12"}}