The metric dimension of small distance-regular and strongly regular graphs

Understand

A {\em resolving set} for a graph $\Gamma$ is a collection of vertices $S$, chosen so that for each vertex $v$, the list of distances from $v$ to the members of $S$ uniquely specifies $v$.

• The {\em metric dimension} of $\Gamma$ is the smallest size of a resolving set for $\Gamma$.
• A graph is {\em distance-regular} if, for any two vertices $u,v$ at each distance $i$, the number of neighbours of $v$ at each possible distance from $u$ (i.e.
• $i-1$, $i$ or $i+1$) depends only on the distance $i$, and not on the choice of vertices $u,v$.