  A vertex $v\in V(G)$ is said to distinguish two vertices $x,y\in V(G)$ of a
nontrivial connected graph $G$ if the distance from $v$ to $x$ is different
from the distance from $v$ to $y$. A set $S\subset V(G)$ is a local metric
generator for $G$ if every two adjacent vertices of $G$ are distinguished by
some vertex of $S$. A local metric generator with the minimum cardinality is
called a local metric basis for $G$ and its cardinality, the local metric
dimension of $G$. It is known that the problem of computing the local metric
dimension of a graph is NP-Complete. In this paper we study the problem of
finding exact values or bounds for the local metric dimension of strong product
of graphs.
