%0 Journal Article 
%A Rodríguez Velázquez, Juan A.
%A González Yero, Ismael
%A Kuziak, Dorota
%A Oellermann, Ortrud
%T On the strong metric dimension of Cartesian and direct products of graphs
%D 2014
%@ 0012-365X
%U http://hdl.handle.net/10498/30926
%X Let $G$ be a connected graph. A vertex $w$ {\em strongly resolves} a pair $u, v$ of vertices of $G$ if there exists some shortest
$u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A set $W$ of vertices is a {\em strong resolving set} for $G$ if every pair of
vertices of $G$ is strongly resolved by some vertex of $W$. The smallest cardinality of a strong resolving set for $G$ is called the {\em strong metric dimension} of $G$. It is known  that the problem of computing the strong metric
dimension of a graph is NP-hard. In this paper we obtain closed formulae for the strong metric dimension of several families of the Cartesian product of graphs and the direct product of graphs.
%K Strong resolving set
%K strong metric dimension
%K Cartesian product of graphs
%K direct product of graphs
%K strong resolving graph
%~ Universidad de Cádiz