The dominant metric dimension of graphs

Liliek Susilowati, Imroatus Sa'adah, Ratna Zaidatul Fauziyyah, Ahmad Erfanian, Slamin

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


The G be a connected graph with vertex set V(G) and edge set E(G). A subset S⊆V(G) is called a dominating set of G if for every vertex x in V(G)∖S, there exists at least one vertex u in S such that x is adjacent to u. An ordered set W⊆V(G) is called a resolving set of G, if every pair of vertices u and v in V(G) have distinct representation with respect to W. An ordered set S⊆V(G) is called a dominant resolving set of G, if S is a resolving set and also a dominating set of G. The minimum cardinality of dominant resolving set is called a dominant metric dimension of G, denoted by Ddim(G). In this paper, we investigate the dominant metric dimension of some particular class of graphs, the characterisation of graph with certain dominant metric dimension, and the dominant metric dimension of joint and comb products of graphs.

Original languageEnglish
Article numbere03633
Issue number3
Publication statusPublished - Mar 2020


  • Dominant metric dimension
  • Dominant resolving set
  • Dominating set
  • Mathematics
  • Metric dimension
  • Resolving set


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