{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T23:44:39Z","timestamp":1649115879537},"reference-count":11,"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":[[2015,3]]},"abstract":"<jats:p> Let R be a commutative ring and Z(R) be the set of all zero-divisors of R. The total graph of R, denoted by T <jats:sub>\u0393<\/jats:sub>(R), is the (undirected) graph with vertices set R. For any two distinct elements x, y \u2208 R, the vertices x and y are adjacent if and only if x + y \u2208 Z(R). In this paper, we obtain certain fundamental properties of the total graph of \u2124<jats:sub>n<\/jats:sub> \u00d7 \u2124<jats:sub>m<\/jats:sub>, where n and m are positive integers. We determine the clique number and independent number of the total graph T <jats:sub>\u0393<\/jats:sub>(\u2124<jats:sub>n<\/jats:sub> \u00d7 \u2124<jats:sub>m<\/jats:sub>). <\/jats:p>","DOI":"10.1142\/s1793830915500044","type":"journal-article","created":{"date-parts":[[2014,12,9]],"date-time":"2014-12-09T02:52:02Z","timestamp":1418093522000},"page":"1550004","source":"Crossref","is-referenced-by-count":1,"title":["Total graph of the ring \u2124<sub>n<\/sub> \u00d7 \u2124<sub>m<\/sub>"],"prefix":"10.1142","volume":"07","author":[{"given":"Alpesh M.","family":"Dhorajia","sequence":"first","affiliation":[{"name":"Birla Institute of Technology and Science, Pilani, Rajasthan 333031, India"}]}],"member":"219","published-online":{"date-parts":[[2015,2,2]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2008.06.028"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1998.7840"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1006\/jabr.1993.1171"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0021-8693(88)90202-5"},{"key":"rf5","volume-title":"Introduction to Graph Theory","author":"Chartrand G.","year":"2006"},{"key":"rf6","volume-title":"Commutative Rings with Zero Divisors","author":"Huckaba J. A.","year":"1988"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgebra.2006.01.019"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1216\/RMJ-2012-42-5-1551"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2006.07.025"},{"key":"rf10","first-page":"177","volume":"2","author":"Smith N. O.","year":"2003","journal-title":"Int. J. Commut. Rings"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1080\/09720529.2011.10698320"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830915500044","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:25:33Z","timestamp":1565137533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830915500044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,2,2]]},"references-count":11,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2015,2,2]]},"published-print":{"date-parts":[[2015,3]]}},"alternative-id":["10.1142\/S1793830915500044"],"URL":"https:\/\/doi.org\/10.1142\/s1793830915500044","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015,2,2]]}}}