The metric dimension 
(Tillquist et al. 2021) or 
(Tomescu and Javid 2007, Ali et al. 2016) of a
graph 
is the smallest number of nodes required to identify all other nodes based on shortest
path distances uniquely. More explicitly, following Foster-Greenwood and Uhl (2022),
let 
be a finite connected graph with vertex
set 
.
For vertices 
,
the graph distance 
is the length of the shortest path between 
and 
in 
. Consider a subset of vertices 
and refer to the vertices in 
as "landmarks." Then 
is called a resolving set if, for every pair of distinct vertices
, there exists a landmark 
such that 
. A resolving set of smallest possible size is
called a metric basis for 
, and the metric dimension of 
is the size of a metric basis.
Tillquist et al. (2021) summarize known results and give closed forms for a number of parametrized families of graphs.
