{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T16:39:21Z","timestamp":1740155961289,"version":"3.37.3"},"reference-count":10,"publisher":"World Scientific Pub Co Pte Ltd","issue":"01","funder":[{"name":"UGC, India"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,2]]},"abstract":"<jats:p> Let [Formula: see text] be a commutative ring with [Formula: see text]. Let [Formula: see text] be a graph with vertices as elements of [Formula: see text], where two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if and only if [Formula: see text] for some non-zero idempotent [Formula: see text] in [Formula: see text]. In this paper, we establish a relation between completeness of the graph [Formula: see text] and regularity of the ring [Formula: see text]. For a finite commutative ring [Formula: see text] with [Formula: see text], we show that the chromatic number of [Formula: see text] is equal to the number of regular elements in [Formula: see text]. Moreover, we characterize some graph theoretic properties of [Formula: see text] and finally we characterize Eulerian property of the graph [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s1793830919500137","type":"journal-article","created":{"date-parts":[[2018,12,2]],"date-time":"2018-12-02T21:36:55Z","timestamp":1543786615000},"page":"1950013","source":"Crossref","is-referenced-by-count":4,"title":["A generalization of co-maximal graph of commutative rings"],"prefix":"10.1142","volume":"11","author":[{"given":"B.","family":"Biswas","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jadavpur University, Kolkata \u2013 700032, India"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3955-9464","authenticated-orcid":false,"given":"S.","family":"Kar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Jadavpur University, Kolkata \u2013 700032, India"}]},{"given":"M. K.","family":"Sen","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, University of Calcutta, Kolkata \u2013 700019, India"}]},{"given":"T. K.","family":"Dutta","sequence":"additional","affiliation":[{"name":"Department of Pure Mathematics, University of Calcutta, Kolkata \u2013 700019, India"}]}],"member":"219","published-online":{"date-parts":[[2019,2,8]]},"reference":[{"key":"S1793830919500137BIB001","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1993.1171"},{"key":"S1793830919500137BIB002","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"S1793830919500137BIB003","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90202-5"},{"key":"S1793830919500137BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0957-8"},{"volume-title":"A First Course in Rings and Ideals","year":"1970","author":"Burton D. M.","key":"S1793830919500137BIB005"},{"volume-title":"Applied and Algorithmic Graph Theory","year":"1993","author":"Chartrand G.","key":"S1793830919500137BIB006"},{"key":"S1793830919500137BIB007","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2007.02.003"},{"key":"S1793830919500137BIB008","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1995.1236"},{"key":"S1793830919500137BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.06.020"},{"volume-title":"Introduction to Graph Theory","year":"2003","author":"West D. B.","key":"S1793830919500137BIB010"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830919500137","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T08:46:29Z","timestamp":1565167589000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830919500137"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,2]]},"references-count":10,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2019,2,8]]},"published-print":{"date-parts":[[2019,2]]}},"alternative-id":["10.1142\/S1793830919500137"],"URL":"https:\/\/doi.org\/10.1142\/s1793830919500137","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"type":"print","value":"1793-8309"},{"type":"electronic","value":"1793-8317"}],"subject":[],"published":{"date-parts":[[2019,2]]}}}