{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,18]],"date-time":"2024-04-18T20:33:27Z","timestamp":1713472407931},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:p> Some concepts in graph theory are resolving set, dominating set, and dominant metric dimension. A resolving set of a connected graph [Formula: see text] is the ordered set [Formula: see text] such that every pair of two vertices [Formula: see text] has the different representation with respect to [Formula: see text]. A Dominating set of [Formula: see text] is the subset [Formula: see text] such that for every vertex [Formula: see text] in [Formula: see text] is adjacent to at least one vertex in [Formula: see text]. A dominant resolving set of [Formula: see text] is an ordered set [Formula: see text] such that [Formula: see text] is a resolving set and a dominating set of [Formula: see text]. The minimum cardinality of a dominant resolving set is called a dominant metric dimension of [Formula: see text], denoted by [Formula: see text]. In this paper, we determine the dominant metric dimension of the joint product graphs. <\/jats:p>","DOI":"10.1142\/s1793830921500105","type":"journal-article","created":{"date-parts":[[2020,8,25]],"date-time":"2020-08-25T14:36:41Z","timestamp":1598366201000},"page":"2150010","source":"Crossref","is-referenced-by-count":1,"title":["On the joint product graphs with respect to dominant metric dimension"],"prefix":"10.1142","volume":"13","author":[{"given":"Liliek","family":"Susilowati","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Airlangga, Surabaya, East Java, Indonesia"}]},{"given":"Imroatus","family":"Sa\u2019adah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Airlangga, Surabaya, East Java, Indonesia"}]},{"given":"Utami Dyah","family":"Purwati","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Airlangga, Surabaya, East Java, Indonesia"}]}],"member":"219","published-online":{"date-parts":[[2020,9,22]]},"reference":[{"issue":"1","key":"S1793830921500105BIB001","doi-asserted-by":"crossref","first-page":"25","DOI":"10.21136\/MB.2003.133935","volume":"128","author":"Brigham R. 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