Abstract
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.
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