{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,2]],"date-time":"2023-03-02T03:42:00Z","timestamp":1677728520826},"reference-count":7,"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":[[2011,9]]},"abstract":"<jats:p> Let D be a dominating set of a graph G = (V, E). For v \u2208 D, let n<jats:sub>1<\/jats:sub>(v) = |N(v) \u2229 (V - D)| and for w \u2208 V - D, let n<jats:sub>2<\/jats:sub>(w) = |N(w) \u2229 D|. Then D is called an equitable dominating set of type 1 if |n<jats:sub>1<\/jats:sub>(v<jats:sub>1<\/jats:sub>) - n<jats:sub>1<\/jats:sub>(v<jats:sub>2<\/jats:sub>)| \u2264 1 for all v<jats:sub>1<\/jats:sub>, v<jats:sub>2<\/jats:sub> \u2208 D and is called an equitable dominating set of type 2 if |n<jats:sub>2<\/jats:sub>(w<jats:sub>1<\/jats:sub>) - n<jats:sub>2<\/jats:sub>(w<jats:sub>2<\/jats:sub>)| \u2264 1 for all w<jats:sub>1<\/jats:sub>, w<jats:sub>2<\/jats:sub> \u2208 V - D. The minimum cardinality of an equitable dominating set of G of type 1 (type 2) is called the 1-equitable (2-equitable) domination number of G and is denoted by \u03b3<jats:sub> eq1 <\/jats:sub>(G)(\u03b3<jats:sub> eq2 <\/jats:sub>(G)). If D is an equitable dominating set of type 1 and type 2, then D is called an equitable dominating set and the equitable domination number of G is defined to be the minimum cardinality of an equitable dominating set and is denoted by \u03b3<jats:sub> eq <\/jats:sub>(G). In this paper we initiate a study of these parameters. <\/jats:p>","DOI":"10.1142\/s1793830911001231","type":"journal-article","created":{"date-parts":[[2011,10,21]],"date-time":"2011-10-21T12:29:23Z","timestamp":1319200163000},"page":"311-321","source":"Crossref","is-referenced-by-count":3,"title":["EQUITABLE DOMINATION IN GRAPHS"],"prefix":"10.1142","volume":"03","author":[{"given":"A.","family":"ANITHA","sequence":"first","affiliation":[{"name":"Department of Mathematics, Thiagarajar College of Engineering, Madurai-625 015, India"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"ARUMUGAM","sequence":"additional","affiliation":[{"name":"National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), Kalasalingam University, Anand Nagar, Krishnankoil-626 126, India"},{"name":"School of Electrical Engineering and Computer Science, The University of Newcastle, NSW 2308, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MUSTAPHA","family":"CHELLALI","sequence":"additional","affiliation":[{"name":"LAMDA-RO Laboratory, Department of Mathematics, University of Blida, B. P. 270, Blida, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1016\/0012-365X(78)90105-X"},{"key":"rf2","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"2005"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1002\/net.3230100304"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(84)90061-1"},{"key":"rf5","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"rf6","volume-title":"Domination in Graphs \u2014 Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"rf7","volume-title":"Complexity of Computer Combinatorial Problems","author":"Karp R. M.","year":"1972"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911001231","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T16:12:48Z","timestamp":1565194368000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911001231"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,9]]},"references-count":7,"journal-issue":{"issue":"03","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,9]]}},"alternative-id":["10.1142\/S1793830911001231"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911001231","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,9]]}}}