%0 Journal Article 
%A Rodríguez Velázquez, Juan A.
%A Kuziak, Dorota
%A González Yero, Ismael
%A Sigarreta Almira, José M.
%T The metric dimension of strong product graphs
%D 2015
%@ 1584-2851
%U http://hdl.handle.net/10498/30930
%X For an ordered subset $S = \{s_1, s_2,\dots s_k\}$ of vertices in a connected graph $G$, the metric representation of a vertex $u$ with respect to the set $S$ is the $k$-vector $ 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 different vertices of $G$ have distinct metric representations with respect to $S$. A minimum metric generator is called a metric basis for $G$ and its cardinality, $dim(G)$, the metric dimension of $G$. It is well known that the problem of finding the metric dimension of a graph is NP-Hard.  In this paper we obtain closed formulae and tight bounds for the metric dimension of strong product graphs.
%K Metric generator
%K metric basis
%K metric dimension
%K strong product graph
%K resolving set
%~ Universidad de Cádiz