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For an ordered subset $S = \{s_1, s_2,\dots s_k\}$ of vertices and a vertex$u$ in a connected graph $G$, the metric representation of $u$ with respect to$S$ is the ordered $k$-tuple $ r(u|S)=(d_G(v,s_1), d_G(v,s_2),\dots,$$d_G(v,s_k))$, where $d_G(x,y)$ represents the distance between the vertices$x$ and $y$. The set $S$ is a metric generator for $G$ if every two differentvertices of $G$ have distinct metric representations. A minimum metricgenerator is called a metric basis for $G$ and its cardinality, $dim(G)$, themetric dimension of $G$. It is well known that the problem of finding themetric dimension of a graph is NP-Hard. In this paper we obtain closed formulaeand tight bounds for the metric dimension of strong product graphs.

The metric dimension of strong product graphs