{
  "id": "2011.12038",
  "version": "v1",
  "published": "2020-11-24T11:31:21.000Z",
  "updated": "2020-11-24T11:31:21.000Z",
  "title": "On metric dimension of digraphs",
  "authors": [
    "Min Feng",
    "Kaishun Wang",
    "Yuefeng Yang"
  ],
  "categories": [
    "math.CO"
  ],
  "abstract": "Using the two way distance, we first introduce resolving sets and metric dimension of a strongly connected digraph $\\Gamma$. Then we establish lower and upper bounds for the number of arcs in $\\Gamma$ by using the diameter and metric dimension of $\\Gamma$, and characterize all digraphs attaining the lower or upper bound. We also study a digraph with metric dimension $1$ and classify all vertex-transitive digraphs having metric dimension $1$. Finally, we characterize all digraphs of order $n$ with metric dimension $n-2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-24T11:31:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C20",
      "05C35"
    ],
    "keywords": [
      "metric dimension",
      "upper bound",
      "way distance",
      "strongly connected digraph",
      "establish lower"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}