{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T11:28:08Z","timestamp":1784633288485,"version":"3.55.0"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2013,3]]},"abstract":"<jats:p> In this paper, we associate the graph \u0393<jats:sub>I<\/jats:sub>(N) to an ideal I of a near-ring N. We exhibit some properties and structure of \u0393<jats:sub>I<\/jats:sub>(N). For a commutative ring R, Beck conjectured that both chromatic number and clique number of the zero-divisor graph \u0393(R) of R are equal. We prove that Beck's conjecture is true for \u0393<jats:sub>I<\/jats:sub>(N). Moreover, we characterize all right permutable near-rings N for which the graph \u0393<jats:sub>I<\/jats:sub>(N) is finitely colorable. <\/jats:p>","DOI":"10.1142\/s1793830913500079","type":"journal-article","created":{"date-parts":[[2013,5,3]],"date-time":"2013-05-03T10:01:57Z","timestamp":1367575317000},"page":"1350007","source":"Crossref","is-referenced-by-count":7,"title":["ZERO-DIVISOR GRAPH OF AN IDEAL OF A NEAR-RING"],"prefix":"10.1142","volume":"05","author":[{"given":"T.","family":"TAMIZH CHELVAM","sequence":"first","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627012, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"NITHYA","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Manonmaniam Sundaranar University, Tirunelveli 627012, India"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2013,5,3]]},"reference":[{"key":"rf1","first-page":"221","volume":"180","author":"Akbari S.","journal-title":"J. Pure Appl. Algebra"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.06.028"},{"key":"rf4","first-page":"61","volume":"220","author":"Anderson D. F.","journal-title":"Lecture Notes in Pure Appl. Math."},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1993.1171"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90202-5"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1007\/BF01300916"},{"key":"rf9","volume-title":"Introduction to Graph theory","author":"Chartrand G.","year":"2006"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1080\/00927870500441858"},{"key":"rf11","volume-title":"Near-rings","author":"Pilz G.","year":"1983"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1081\/AGB-120022801"},{"key":"rf13","first-page":"1957","volume":"38","author":"Satyanarayana Bh.","journal-title":"Commun. Algebra"},{"key":"rf14","first-page":"341","volume":"32","author":"Chelvam T. Tamizh","journal-title":"Discuss. Math. Graph Theory"},{"key":"rf15","volume":"41","author":"Chelvam T. Tamizh","journal-title":"Commun. Algebra"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1080\/00927879208824479"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830913500079","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T20:17:07Z","timestamp":1565122627000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830913500079"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,3]]},"references-count":15,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2013,5,3]]},"published-print":{"date-parts":[[2013,3]]}},"alternative-id":["10.1142\/S1793830913500079"],"URL":"https:\/\/doi.org\/10.1142\/s1793830913500079","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,3]]}}}