@inproceedings{dc036ce97f9b4f4aab4133ef816b8705,

title = "On the metric dimension of Cartesian products of graphs",

abstract = "A set of vertices S resolves a graph G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G □ H. We prove that the metric dimension of G□G is tied in a strong sense to the minimum order of a so-called doubly resolving set in G. Using bounds on the order of doubly resolving sets, we establish bounds on G □ H for many examples of G and H. One of our main results is a family of graphs G with bounded metric dimension for which the metric dimension of G□G is unbounded.",

author = "J. C{\'a}ceres and C. Hernando and Merce Mora and Pelayo, {I. M.} and Puertas, {M. L.} and C. Seara and Wood, {D. R.}",

year = "2006",

language = "English",

volume = "23",

series = "Ciencias (Valladolid)",

publisher = "Univ. Valladolid, Secr. Publ. Intercamb. Ed., Valladolid",

pages = "195--202",

booktitle = "Fifth Conference on Discrete Mathematics and Computer Science (Spanish)",

}