Abstract
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 language | English |
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Pages (from-to) | 461-472 |
Number of pages | 12 |
Journal | Bulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie |
Volume | 52 |
Issue number | 4 |
Publication status | Published - 2009 |
Externally published | Yes |
Keywords
- Induced subgraph
- Infinite regular graph
- Metric dimension
- Partition dimension
- Plane tiling
ASJC Scopus subject areas
- General Mathematics