On Metric and Partition Dimensions of Some Inflnite Regular Graphs
Ioan Tomescu, Muhammad Imran · 2009
In this paper some inflnite regular graphs generated by tilings of the plane by regular triangles and hexagons are considered. These graphs have no flnite metric bases but their partition dimension is flnite and is evaluated in some cases. Also, it is proved that for every n ‚ 2 there exists flnite induced subgraphs of these graphs having metric dimension equal to n as well as inflnite induced subgraphs with metric dimension equal to three.