On metric and partition dimensions of some infinite regular graphs

Ioan Tomescu, Muhammad Imran

Research output: Contribution to journalArticlepeer-review

51 Citations (Scopus)


In this paper some infinite regular graphs generated by tilings of the plane by regular triangles and hexagons are considered. These graphs have no finite metric bases but their partition dimension is finite and is evaluated in some cases. Also, it is proved that for every n ≥ 2 there exists finite induced subgraphs of these graphs having metric dimension equal to n as well as infinite induced subgraphs with metric dimension equal to three.

Original languageEnglish
Pages (from-to)461-472
Number of pages12
JournalBulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Issue number4
Publication statusPublished - 2009
Externally publishedYes


  • Induced subgraph
  • Infinite regular graph
  • Metric dimension
  • Partition dimension
  • Plane tiling

ASJC Scopus subject areas

  • General Mathematics


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