{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T00:24:16Z","timestamp":1778804656220,"version":"3.51.4"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> In this paper we study zero-divisor graphs of rings and semirings. We show that all zero-divisor graphs of (possibly noncommutative) semirings are connected and have diameter less than or equal to 3. We characterize all acyclic zero-divisor graphs of semirings and prove that in the case zero-divisor graphs are cyclic, their girths are less than or equal to 4. We find all possible cyclic zero-divisor graphs over commutative semirings having at most one 3-cycle, and characterize all complete k-partite and regular zero-divisor graphs. Moreover, we characterize all additively cancellative commutative semirings and all commutative rings such that their zero-divisor graph has exactly one 3-cycle. <\/jats:p>","DOI":"10.1142\/s0218196712500336","type":"journal-article","created":{"date-parts":[[2012,2,6]],"date-time":"2012-02-06T00:47:00Z","timestamp":1328489220000},"page":"1250033","source":"Crossref","is-referenced-by-count":18,"title":["THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS"],"prefix":"10.1142","volume":"22","author":[{"given":"DAVID","family":"DOL\u017dAN","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"POLONA","family":"OBLAK","sequence":"additional","affiliation":[{"name":"Faculty of Computer and Information Science, University of Ljubljana, Tr\u017ea\u0161ka 25, SI-1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00435-6"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.07.007"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.02.051"},{"key":"rf4","first-page":"361","volume":"34","author":"Anderson D. 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