{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T05:11:53Z","timestamp":1648789913588},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2017,8]]},"abstract":"<jats:p> In this paper, we study the infinite graphs which admit a finite dominating set. The main contribution of the work is two folds: (i) characterization of infinite trees and hence infinite connected graphs with a finite dominating set, (ii) it is shown that apart from a family of graphs, all infinite graphs or their complements possess a finite dominating set. Moreover, some conditions of existence of finite dominating sets in product graphs are studied. <\/jats:p>","DOI":"10.1142\/s1793830917500537","type":"journal-article","created":{"date-parts":[[2017,7,10]],"date-time":"2017-07-10T06:49:02Z","timestamp":1499669342000},"page":"1750053","source":"Crossref","is-referenced-by-count":1,"title":["Infinite graphs with finite dominating sets"],"prefix":"10.1142","volume":"09","author":[{"given":"Angsuman","family":"Das","sequence":"first","affiliation":[{"name":"Department of Mathematics, St. Xavier\u2019s College, Kolkata, India"}]}],"member":"219","published-online":{"date-parts":[[2017,8,16]]},"reference":[{"key":"S1793830917500537BIB001","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2009.11.007"},{"key":"S1793830917500537BIB002","series-title":"Topics in Discrete Mathematics","volume-title":"Directions in Infinite Graph Theory and Combinatorics","volume":"3","author":"Diestel R.","year":"1992"},{"key":"S1793830917500537BIB003","series-title":"Graduate Texts in Mathematics","volume-title":"Graph Theory","volume":"173","author":"Diestel R.","year":"2016","edition":"5"},{"key":"S1793830917500537BIB004","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S1793830917500537BIB005","volume-title":"Domination in Graphs: Advanced Topics","author":"Haynes T. W.","year":"1998"},{"key":"S1793830917500537BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0021-9800(67)80077-2"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830917500537","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T13:03:23Z","timestamp":1565096603000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830917500537"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,8]]},"references-count":6,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2017,8,16]]},"published-print":{"date-parts":[[2017,8]]}},"alternative-id":["10.1142\/S1793830917500537"],"URL":"https:\/\/doi.org\/10.1142\/s1793830917500537","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,8]]}}}