{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,12]],"date-time":"2026-04-12T14:20:28Z","timestamp":1776003628754,"version":"3.50.1"},"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 defensive alliance in a graph $G = (V,E)$ is a set of vertices $S \\subseteq V$ satisfying the condition that for every vertex $v \\in S$, the number of neighbors $v$ has in $S$ plus one (counting $v$) is at least as large as the number of neighbors it has in $V-S$. Because of such an alliance, the vertices in $S$, agreeing to mutually support each other, have the strength of numbers to be able to defend themselves from the vertices in $V-S$. A defensive alliance $S$ is called global if it effects every vertex in $V-S$, that is, every vertex in $V-S$ is adjacent to at least one member of the alliance $S$. Note that a global defensive alliance is  a dominating set.  We study global defensive alliances in graphs.<\/jats:p>","DOI":"10.37236\/1740","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:02:41Z","timestamp":1578639761000},"source":"Crossref","is-referenced-by-count":51,"title":["Global Defensive Alliances in Graphs"],"prefix":"10.37236","volume":"10","author":[{"given":"Teresa W.","family":"Haynes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stephen T.","family":"Hedetniemi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael A.","family":"Henning","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2003,12,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r47\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r47\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:05:22Z","timestamp":1579323922000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r47"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,12,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1740","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003,12,8]]},"article-number":"R47"}}