{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:04:01Z","timestamp":1777367041791,"version":"3.51.4"},"reference-count":33,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2014,12]]},"abstract":"<jats:p> Let R be a commutative ring with identity which is not an integral domain. An ideal I of a ring R is called an annihilating ideal if there exists r \u2208 R\\{0} such that Ir = (0). In this paper, we consider a simple undirected graph associated with R denoted by \u03a9(R) whose vertex set equals the set of all nonzero annihilating ideals of R and two distinct vertices I, J in this graph are joined by an edge if and only if I + J is also an annihilating ideal of R. In this paper, for any ring R which is not an integral domain, the problem of when \u03a9(R) is connected is discussed and if \u03a9(R) is connected, then it is shown that diam (\u03a9(R)) \u2264 2. Moreover, it is verified that gr (\u03a9(R)) \u2208 {3, \u221e}. Furthermore, rings R such that \u03c9(\u03a9(R)) &lt; \u221e are characterized. <\/jats:p>","DOI":"10.1142\/s1793830914500475","type":"journal-article","created":{"date-parts":[[2014,6,2]],"date-time":"2014-06-02T01:01:11Z","timestamp":1401670871000},"page":"1450047","source":"Crossref","is-referenced-by-count":20,"title":["A graph associated with the set of all nonzero annihilating ideals of a commutative ring"],"prefix":"10.1142","volume":"06","author":[{"given":"S.","family":"Visweswaran","sequence":"first","affiliation":[{"name":"Department of Mathematics, Saurashtra University, Rajkot, 360005, Gujarat, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hiren D.","family":"Patel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Saurashtra University, Rajkot, 360005, Gujarat, India"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2014,10,10]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.10.020"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.4134\/JKMS.2012.49.1.085"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2009.03.013"},{"key":"rf4","first-page":"13","volume":"12","author":"Akbari S.","year":"2013","journal-title":"J. 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