{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T02:42:39Z","timestamp":1649040159866},"reference-count":5,"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":[[2011,3]]},"abstract":"<jats:p> In this paper, we introduce the concept called upper and lower independence number of a graph. The amount of independenceness of a vertex is calculated first. With the help of independenceness of vertices, we find the independence number of a graph. The main focus of this paper is to extend the dominating chain ir (G) \u2264 \u03b3(G) \u2264 i(G) \u2264 \u03b2<jats:sub>0<\/jats:sub>(G) \u2264 \u0393(G) \u2264 IR (G), mentioned in [Haynes, Hedetniemi and Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998)]. <\/jats:p>","DOI":"10.1142\/s1793830911001012","type":"journal-article","created":{"date-parts":[[2011,4,14]],"date-time":"2011-04-14T09:45:47Z","timestamp":1302774347000},"page":"53-61","source":"Crossref","is-referenced-by-count":0,"title":["THE UPPER AND LOWER INDEPENDENCE NUMBER OF GRAPHS"],"prefix":"10.1142","volume":"03","author":[{"given":"G.","family":"MARIMUTHU","sequence":"first","affiliation":[{"name":"Department of Mathematics, The Madura College, Madurai 625011, Tamil Nadu, India"}]},{"given":"M. SIVANANDHA","family":"SARASWATHY","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Thiagarajar College of Engineering, Madurai 625006, Tamil Nadu, India"}]},{"given":"G. UMA","family":"MAHESHWARI","sequence":"additional","affiliation":[{"name":"Gandhigram Rural University, Gandhigram, Dindigul, Tamil Nadu, India"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","first-page":"613","volume":"75","author":"Bonchev D.","journal-title":"Croat. Chem. Acta"},{"key":"rf2","volume-title":"Distance in Graphs","author":"Buckley F.","year":"1990"},{"key":"rf3","first-page":"31","volume":"63","author":"Gutman I.","journal-title":"Publ. Inst. Math. (Beograd)"},{"key":"rf4","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"rf5","first-page":"5","volume":"27","author":"Zhou B.","journal-title":"Kragujevac J. Math."}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911001012","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T01:32:20Z","timestamp":1565141540000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911001012"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,3]]},"references-count":5,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,3]]}},"alternative-id":["10.1142\/S1793830911001012"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911001012","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,3]]}}}