{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T11:03:05Z","timestamp":1770980585653,"version":"3.50.1"},"reference-count":17,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p> Let [Formula: see text] be a commutative ring with identity and [Formula: see text] be the set of ideals with nonzero annihilator. The strongly annihilating-ideal graph of [Formula: see text] is defined as the graph [Formula: see text] with the vertex set [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] and [Formula: see text]. It is proved that [Formula: see text] is connected with diameter at most two and with girth at most four, if it contains a cycle. Moreover, we characterize all rings whose strongly annihilating-ideal graphs are complete or star. Furthermore, we study the affinity between strongly annihilating-ideal graph and annihilating-ideal graph (a well-known graph with the same vertices and two distinct vertices [Formula: see text] are adjacent if and only if [Formula: see text]) associated with a commutative ring. <\/jats:p>","DOI":"10.1142\/s1793830917500288","type":"journal-article","created":{"date-parts":[[2017,2,17]],"date-time":"2017-02-17T03:08:26Z","timestamp":1487300906000},"page":"1750028","source":"Crossref","is-referenced-by-count":6,"title":["On the strongly annihilating-ideal graph of a commutative ring"],"prefix":"10.1142","volume":"09","author":[{"given":"N. Kh.","family":"Tohidi","sequence":"first","affiliation":[{"name":"Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran"}]},{"given":"M. J.","family":"Nikmehr","sequence":"additional","affiliation":[{"name":"Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran"}]},{"given":"R.","family":"Nikandish","sequence":"additional","affiliation":[{"name":"Department of Basic Sciences, Jundi-Shapur University of Technology, Dezful, Iran"}]}],"member":"219","published-online":{"date-parts":[[2017,4,13]]},"reference":[{"key":"S1793830917500288BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.10.020"},{"key":"S1793830917500288BIB002","doi-asserted-by":"publisher","DOI":"10.4134\/JKMS.2015.52.2.417"},{"key":"S1793830917500288BIB003","first-page":"831","volume":"29","author":"Anderson D. D.","year":"2003","journal-title":"Houston J. 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