{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T07:07:13Z","timestamp":1648883233901},"reference-count":18,"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":[[2016,6]]},"abstract":"<jats:p> Let [Formula: see text] be a commutative ring with identity. In this paper, we consider a simple graph associated with [Formula: see text] denoted by [Formula: see text], whose vertex set is the set of all nonzero proper ideals of [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent whenever [Formula: see text] or [Formula: see text]. In this paper, we initiate the study of the graph [Formula: see text] and we investigate its properties. In particular, we show that [Formula: see text] is a connected graph with [Formula: see text] unless [Formula: see text] is isomorphic to a direct product of two fields. Moreover, we characterize all commutative rings [Formula: see text] with at least two maximal ideals for which [Formula: see text] are planar. <\/jats:p>","DOI":"10.1142\/s1793830916500294","type":"journal-article","created":{"date-parts":[[2016,2,18]],"date-time":"2016-02-18T05:28:32Z","timestamp":1455773312000},"page":"1650029","source":"Crossref","is-referenced-by-count":4,"title":["A new graph associated to a commutative ring"],"prefix":"10.1142","volume":"08","author":[{"given":"A.","family":"Alilou","sequence":"first","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J.","family":"Amjadi","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. M.","family":"Sheikholeslami","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2016,5,26]]},"reference":[{"key":"S1793830916500294BIB001","doi-asserted-by":"publisher","DOI":"10.1142\/S1005386714000200"},{"key":"S1793830916500294BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2011.10.020"},{"key":"S1793830916500294BIB003","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-2013-43-5-1415"},{"key":"S1793830916500294BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00370-3"},{"key":"S1793830916500294BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-8693(03)00435-6"},{"key":"S1793830916500294BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2005.07.007"},{"key":"S1793830916500294BIB007","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2012.753606"},{"key":"S1793830916500294BIB008","series-title":"Lecture Notes in Pure and Applied Mathematics","first-page":"61","volume-title":"Ideal Theoretic Methods in Commutative Algebra","volume":"220","author":"Anderson D. F.","year":"2001"},{"key":"S1793830916500294BIB009","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"S1793830916500294BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.jpaa.2006.10.007"},{"key":"S1793830916500294BIB011","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1993.1171"},{"key":"S1793830916500294BIB012","volume-title":"Introduction to Commutative Algebra","author":"Atiyah M. F.","year":"1969"},{"key":"S1793830916500294BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90202-5"},{"key":"S1793830916500294BIB014","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811004896"},{"key":"S1793830916500294BIB015","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498811004902"},{"key":"S1793830916500294BIB016","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1972-0294316-2"},{"key":"S1793830916500294BIB017","doi-asserted-by":"publisher","DOI":"10.1142\/S1793830914500475"},{"key":"S1793830916500294BIB018","volume-title":"Introduction to Graph Theory","author":"West D. B.","year":"2001","edition":"2"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830916500294","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:04:48Z","timestamp":1565125488000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830916500294"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,5,26]]},"references-count":18,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2016,5,26]]},"published-print":{"date-parts":[[2016,6]]}},"alternative-id":["10.1142\/S1793830916500294"],"URL":"https:\/\/doi.org\/10.1142\/s1793830916500294","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,5,26]]}}}