{
  "id": "1903.11933",
  "version": "v1",
  "published": "2019-03-28T13:05:00.000Z",
  "updated": "2019-03-28T13:05:00.000Z",
  "title": "Metric dimension of maximal outerplanar graphs",
  "authors": [
    "Mercè Claverol",
    "Alfredo García",
    "Greogorio Hernández",
    "Carmen Hernando",
    "Montserrat Maureso",
    "Mercè Mora",
    "Javier Tejel"
  ],
  "comment": "25 pages, 16 figures",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, we study the metric dimension problem in maximal outerplanar graphs. Concretely, if $\\beta (G)$ is the metric dimension of a maximal outerplanar graph $G$ of order $n$, we prove that $2\\le \\beta (G) \\le \\lceil \\frac{2n}{5}\\rceil$ and that the bounds are tight. We also provide linear algorithms to decide whether the metric dimension of $G$ is 2 and to build a resolving set of size $\\lceil \\frac{2n}{5}\\rceil$ for $G$. Moreover, we characterize the maximal outerplanar graphs with metric dimension 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-28T13:05:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "05C62"
    ],
    "keywords": [
      "maximal outerplanar graph",
      "metric dimension problem",
      "linear algorithms",
      "resolving set"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 25,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}