{
  "id": "math/0507527",
  "version": "v3",
  "published": "2005-07-26T09:30:57.000Z",
  "updated": "2006-03-02T11:44:27.000Z",
  "title": "On the Metric Dimension of Cartesian Products of Graphs",
  "authors": [
    "José Cáceres",
    "Carmen Hernando",
    "Mercé Mora",
    "Ignacio M. Pelayo",
    "María L. Puertas",
    "Carlos Seara",
    "David R. Wood"
  ],
  "journal": "SIAM J. Discrete Mathematics, 21(2):423-441, 2007",
  "doi": "10.1137/050641867",
  "categories": [
    "math.CO"
  ],
  "abstract": "A set S of vertices in a graph G resolves 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.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2006-03-02T11:44:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12"
    ],
    "keywords": [
      "cartesian products",
      "doubly resolving set",
      "minimum cardinality",
      "minimum order",
      "strong sense"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......7527C"
    }
  }
}