On the joint product graphs with respect to dominant metric dimension

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2 Citations (Scopus)


Some concepts in graph theory are resolving set, dominating set, and dominant metric dimension. A resolving set of a connected graph G is the ordered set W ⊆ V (G) such that every pair of two vertices u,v V (G) has the different representation with respect to W. A Dominating set of G is the subset S ⊆ V (G) such that for every vertex x in V (G)\S is adjacent to at least one vertex in S. A dominant resolving set of G is an ordered set W ⊆ V (G) such that W is a resolving set and a dominating set of G. The minimum cardinality of a dominant resolving set is called a dominant metric dimension of G, denoted by Ddim(G). In this paper, we determine the dominant metric dimension of the joint product graphs.

Original languageEnglish
Article number2150010
JournalDiscrete Mathematics, Algorithms and Applications
Issue number2
Publication statusPublished - Apr 2021


  • Connected graph
  • dominant metric dimension
  • dominant resolving set
  • dominating set
  • joint product graph
  • ordered set
  • resolving set


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