{
  "id": "1602.08907",
  "version": "v1",
  "published": "2016-02-29T11:16:38.000Z",
  "updated": "2016-02-29T11:16:38.000Z",
  "title": "On the Partition Dimension and the Twin Number of a Graph",
  "authors": [
    "Carmen Hernando",
    "Merce mora",
    "Ignacio M Pelayo"
  ],
  "comment": "21 pages, 7 figures, 2 tables, 19 references",
  "categories": [
    "math.CO"
  ],
  "abstract": "A partition P of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of P. The partition dimension of G is the minimum cardinality of a locating partition of G. A pair of vertices u,v of a graph G are called twins if they have exactly the same set of neighbors other than u and v. A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G. In this paper we undertake the study of the partition dimension of a graph by also considering its twin number. This approach allows us to obtain the set of connected graphs of order n having partition dimension n-2. This set is formed by exactly 15 graphs, instead of 23, as was wrongly stated in the paper: \"Discrepancies between metric dimension and partition dimension of a connected graph\", published in Discrete Mathematics in 2008.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-29T11:16:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C35"
    ],
    "keywords": [
      "partition dimension",
      "twin number",
      "connected graph",
      "twin class",
      "locating partition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}