{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:48:19Z","timestamp":1759063699504,"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>A global defensive alliance in a graph $G=(V,E)$ is a dominating set $S$ satisfying the condition that for every vertex $v\\in S$, $|N[v]\\cap S|\\geq |N(v)\\cap(V-S)|$. In this note, a new upper bound on the global defensive alliance number of a tree  is given in terms of its order and the number of support vertices. Moreover, we characterize trees attaining this upper bound.<\/jats:p>","DOI":"10.37236\/689","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:41:03Z","timestamp":1578714063000},"source":"Crossref","is-referenced-by-count":1,"title":["A New Upper Bound on the Global Defensive Alliance Number in Trees"],"prefix":"10.37236","volume":"18","author":[{"given":"Xue-gang","family":"Chen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wai Chee","family":"Shiu","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,10,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p202\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p202\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:00:56Z","timestamp":1579302056000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p202"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,10]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/689","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,10]]},"article-number":"P202"}}