The metric dimension of strong product graphs

Identifier:  imarina:5128958

Handle: https://hdl.handle.net/20.500.11797/imarina5128958

Authors:  Rodriguez-Velazquez, Juan A; Kuziak, Dorota; Yero, Ismael G; Sigarreta, Jose M

Abstract:
For an ordered subset S = {s1; s2; ¿ sk} 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) = (dG(v, s1); dG(v; s2); ¿; dG(v; sk)), where dG(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. © 2015, North University of Baia Mare. All rights reserved.