{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,1,31]],"date-time":"2023-01-31T17:20:48Z","timestamp":1675185648606},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["New Math. and Nat. Computation"],"published-print":{"date-parts":[[2016,3]]},"abstract":"<jats:p> Let [Formula: see text] be a fuzzy graph on a finite set [Formula: see text] Let [Formula: see text] and [Formula: see text] A fuzzy subset [Formula: see text] of [Formula: see text] is called an [Formula: see text]-fuzzy dominating set ([Formula: see text]-FD set) of G if [Formula: see text] Then [Formula: see text] is called the [Formula: see text]-fuzzy domination number of [Formula: see text] where the minimum is taken over all [Formula: see text]-FD sets [Formula: see text] of [Formula: see text] In this paper we initiate a study of this parameter and other related concepts such as [Formula: see text]-fuzzy irredundance and [Formula: see text]-fuzzy independence. We obtain the [Formula: see text]-fuzzy domination chain which is analogous to the domination chain in crisp graphs. <\/jats:p>","DOI":"10.1142\/s1793005716500010","type":"journal-article","created":{"date-parts":[[2016,4,7]],"date-time":"2016-04-07T05:19:37Z","timestamp":1460006377000},"page":"1-10","source":"Crossref","is-referenced-by-count":1,"title":["On (<i>r,s<\/i>)-Fuzzy Domination in Fuzzy Graphs"],"prefix":"10.1142","volume":"12","author":[{"given":"S.","family":"Arumugam","sequence":"first","affiliation":[{"name":"National Centre for Advanced Research in Discrete Mathematics, Kalasalingam University, Anand Nagar, Krishnankoil 626 126, Tamil Nadu, India"}]},{"given":"Kiran","family":"Bhutani","sequence":"additional","affiliation":[{"name":"Department of Mathematics, The Catholic University of America, Washington DC 20064, USA"}]},{"given":"L.","family":"Sathikala","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Ramco Institute of Technology, Rajapalayam-626 117, Tamil Nadu, India"}]}],"member":"219","published-online":{"date-parts":[[2016,4,6]]},"reference":[{"key":"S1793005716500010BIB001","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"2005","edition":"4"},{"key":"S1793005716500010BIB002","doi-asserted-by":"publisher","DOI":"10.1016\/S0012-365X(96)00356-1"},{"key":"S1793005716500010BIB003","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1978-079-5"},{"key":"S1793005716500010BIB004","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(93)90288-5"},{"key":"S1793005716500010BIB005","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S1793005716500010BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-7908-1854-3"},{"key":"S1793005716500010BIB008","first-page":"77","volume-title":"In Fuzzy sets and their applications","author":"Rosenfeld A.","year":"1975"},{"key":"S1793005716500010BIB009","doi-asserted-by":"publisher","DOI":"10.1016\/S0167-8655(98)00064-6"},{"key":"S1793005716500010BIB010","volume-title":"Fractional Graph Theory: A Rational Approch to the Theory of Graphs","author":"Scheinerman E. R.","year":"1997"}],"container-title":["New Mathematics and Natural Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793005716500010","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:36:35Z","timestamp":1565098595000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793005716500010"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,3]]},"references-count":9,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2016,4,6]]},"published-print":{"date-parts":[[2016,3]]}},"alternative-id":["10.1142\/S1793005716500010"],"URL":"https:\/\/doi.org\/10.1142\/s1793005716500010","relation":{},"ISSN":["1793-0057","1793-7027"],"issn-type":[{"value":"1793-0057","type":"print"},{"value":"1793-7027","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,3]]}}}