## Abstract

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 language | English |
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Article number | 2150010 |

Journal | Discrete Mathematics, Algorithms and Applications |

Volume | 13 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 2021 |

## Keywords

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