{
  "id": "2202.00716",
  "version": "v1",
  "published": "2022-02-01T19:15:43.000Z",
  "updated": "2022-02-01T19:15:43.000Z",
  "title": "Metric dimension of lexicographic product of some known graphs",
  "authors": [
    "Mohsen Jannesari"
  ],
  "comment": "10 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "For an ordered set W = {w1,w2,...,wk} of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W) := (d(v,w1),d(v,w2),...,d(v,wk)) is called the (metric) representation of v with respect to W, where d(x,y) is the distance between the vertices x and y. The set W is called a resolving set for G if distinct vertices of G have distinct representations with respect to W. The minimum cardinality of a resolving set for G is its metric dimension. In this paper, we investigate the metric dimension of the lexicographic product of graphs G and H, G[H] for some known graphs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-01T19:15:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric dimension",
      "lexicographic product",
      "resolving set",
      "distinct vertices",
      "distinct representations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}