{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T23:01:41Z","timestamp":1648508501897},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2020,6]]},"abstract":"<jats:p> Let [Formula: see text] be a commutative ring with unity. The cozero-divisor graph of [Formula: see text] denoted by [Formula: see text] is a graph with the vertex set [Formula: see text], where [Formula: see text] is the set of all nonzero and non-unit elements of [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]. Let [Formula: see text] and [Formula: see text] denote the clique number and the chromatic number of [Formula: see text], respectively. In this paper, we prove that if [Formula: see text] is a finite commutative ring, then [Formula: see text] is perfect. Also, we prove that if [Formula: see text] is a commutative Artinian non-local ring and [Formula: see text] is finite, then [Formula: see text]. For Artinian local ring, we obtain an upper bound for the chromatic number of cozero-divisor graph. Among other results, we prove that if [Formula: see text] is a commutative ring, then [Formula: see text] is a complete bipartite graph if and only if [Formula: see text], where [Formula: see text] and [Formula: see text] are fields. Moreover, we present some results on the complete [Formula: see text]-partite cozero-divisor graphs. <\/jats:p>","DOI":"10.1142\/s1793830920500238","type":"journal-article","created":{"date-parts":[[2019,12,26]],"date-time":"2019-12-26T04:25:30Z","timestamp":1577334330000},"page":"2050023","source":"Crossref","is-referenced-by-count":0,"title":["The coloring of the cozero-divisor graph of a commutative ring"],"prefix":"10.1142","volume":"12","author":[{"given":"S.","family":"Akbari","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran"}]},{"given":"S.","family":"Khojasteh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran"}]}],"member":"219","published-online":{"date-parts":[[2020,5,28]]},"reference":[{"issue":"1","key":"S1793830920500238BIB001","first-page":"753","volume":"35","author":"Afkhami M.","year":"2011","journal-title":"Southeast Asian Bull. Math."},{"key":"S1793830920500238BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498813501132"},{"key":"S1793830920500238BIB003","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498813500564"},{"key":"S1793830920500238BIB004","doi-asserted-by":"publisher","DOI":"10.1080\/00927872.2012.745867"},{"key":"S1793830920500238BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.06.028"},{"key":"S1793830920500238BIB006","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"S1793830920500238BIB007","volume-title":"Introduction to Commutative Algebra","author":"Atiyeh M. F.","year":"1969"},{"key":"S1793830920500238BIB008","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2006.164.51"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830920500238","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,7,8]],"date-time":"2020-07-08T10:49:06Z","timestamp":1594205346000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830920500238"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,5,28]]},"references-count":8,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2020,6]]}},"alternative-id":["10.1142\/S1793830920500238"],"URL":"https:\/\/doi.org\/10.1142\/s1793830920500238","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,5,28]]}}}