{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T03:48:53Z","timestamp":1774583333367,"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>The annihilation number $a$ of a graph is an upper bound of the independence number $\\alpha$ of a graph.  In this article we characterize graphs with equal independence and annihilation numbers. In particular, we show that $\\alpha=a$ if, and only if, either (1) $a\\geq \\frac{n}{2}$ and $\\alpha' =a$, or (2) $a &lt; \\frac{n}{2}$ and there is a vertex $v\\in V(G)$ such that $\\alpha' (G-v)=a(G)$, where $\\alpha'$ is the critical independence number of the graph. Furthermore, we show that it can be determined in polynomial time whether $\\alpha=a$. Finally we show that a graph where $\\alpha=a$ is either K\u00f6nig-Egerv\u00e1ry or almost K\u00f6nig-Egerv\u00e1ry.<\/jats:p>","DOI":"10.37236\/667","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:42:27Z","timestamp":1578714147000},"source":"Crossref","is-referenced-by-count":12,"title":["Graphs with equal Independence and Annihilation Numbers"],"prefix":"10.37236","volume":"18","author":[{"given":"C. E.","family":"Larson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R.","family":"Pepper","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,9,9]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p180\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p180\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:02:07Z","timestamp":1579302127000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p180"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9,9]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/667","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9,9]]},"article-number":"P180"}}