Narrow Results

Let $H=(V,E)$ be a connected graph of size $n$. If $W$ is an ordered subset of distinct vertices in $H$ then the subset $W$ is said to be a resolving set for $H$, if all of the vertices in the graph can be uniquely defined by the vector of distances to the vertices in $W$. A resolving set $W$ with minimum possible vertices is said to be a metric basis for $H$. The cardinality of the metric basis is called the metric dimension of the graph $H$. In this paper, we demonstrate that the metric dimension for some families of related planar graphs is three.