{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T01:41:46Z","timestamp":1722994906299},"reference-count":6,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:p> For a set [Formula: see text] of vertices of a graph [Formula: see text], the representation multiset of a vertex [Formula: see text] of [Formula: see text] with respect to [Formula: see text] is [Formula: see text], where [Formula: see text] is a distance between of the vertex [Formula: see text] and the vertices in [Formula: see text] together with their multiplicities. The set [Formula: see text] is a resolving set of [Formula: see text] if [Formula: see text] for every pair [Formula: see text] of distinct vertices of [Formula: see text]. The minimum resolving set [Formula: see text] is a multiset basis of [Formula: see text]. If [Formula: see text] has a multiset basis, then its cardinality is called multiset dimension, denoted by [Formula: see text]. A set [Formula: see text] of vertices in [Formula: see text] is a dominating set for [Formula: see text] if every vertex of [Formula: see text] that is not in [Formula: see text] is adjacent to some vertex of [Formula: see text]. The minimum cardinality of the dominating set is a domination number, denoted by [Formula: see text]. A vertex set of some vertices in [Formula: see text] that is both resolving and dominating set is a resolving dominating set. The minimum cardinality of resolving dominating set is called resolving domination number, denoted by [Formula: see text]. In our paper, we investigate and establish sharp bounds of the resolving domination number of [Formula: see text] and determine the exact value of some family graphs. <\/jats:p>","DOI":"10.1142\/s179383091950071x","type":"journal-article","created":{"date-parts":[[2019,9,27]],"date-time":"2019-09-27T03:13:48Z","timestamp":1569554028000},"page":"1950071","source":"Crossref","is-referenced-by-count":7,"title":["Resolving domination number of graphs"],"prefix":"10.1142","volume":"11","author":[{"given":"Ridho","family":"Alfarisi","sequence":"first","affiliation":[{"name":"Department of Primary School, University of Jember, Jember, East Java, Indonesia"}]},{"family":"Dafik","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, University of Jember, Jember, East Java, Indonesia"}]},{"given":"Arika Indah","family":"Kristiana","sequence":"additional","affiliation":[{"name":"Department of Mathematics Education, University of Jember, Jember, East Java, Indonesia"}]}],"member":"219","published-online":{"date-parts":[[2019,12,19]]},"reference":[{"key":"S179383091950071XBIB001","volume-title":"Graphs and Digraphs","author":"Chartrand G.","year":"2000","edition":"3"},{"key":"S179383091950071XBIB002","volume-title":"Handbook of Graph Theory","author":"Gross J. L.","year":"2014","edition":"2"},{"key":"S179383091950071XBIB003","first-page":"191","volume":"2","author":"Harary F.","year":"1976","journal-title":"Ars Combin"},{"key":"S179383091950071XBIB004","volume-title":"Pearls in Graph Theory","author":"Hartsfield N.","year":"1994"},{"key":"S179383091950071XBIB005","volume-title":"Fundamentals of Domination in Graphs","author":"Haynes T. W.","year":"1998"},{"key":"S179383091950071XBIB006","first-page":"549","volume":"14","author":"Slater P. J.","year":"1975","journal-title":"Proc. 6th Southeast Conf. Comb., Graph Theory, Comput. Boca Rotan"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S179383091950071X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,20]],"date-time":"2019-12-20T01:43:53Z","timestamp":1576806233000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S179383091950071X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":6,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1142\/S179383091950071X"],"URL":"https:\/\/doi.org\/10.1142\/s179383091950071x","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,12]]}}}