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.



Additional Information


Kuziak, Dorota, Rodríguez-Velázquez, Juan A., Sigarreta, José M., Yero, Ismael G.