{
  "id": "2407.07851",
  "version": "v1",
  "published": "2024-07-10T17:13:05.000Z",
  "updated": "2024-07-10T17:13:05.000Z",
  "title": "Edge and mixed metric dimension of Johnson graphs",
  "authors": [
    "Jozef Kratica",
    "Mirjana Cangalović",
    "Vera Kovačević-Vujčić",
    "Milica Milivojević Danas"
  ],
  "comment": "14 pages",
  "categories": [
    "math.CO"
  ],
  "abstract": "In this paper, both edge and mixed metric dimensions of Johnson graphs $J_{n,k}$ are considered. A new tight lower bound for $\\beta_E(J_{n,k})$ based on hitting sets has been obtained. Using this bound, exact values for $\\beta_E(J_{n,2})$ and $\\beta_M(J_{n,2})$ have been derived, and it is proved that $\\beta_E(J_{n,2}) = \\beta_M(J_{n,2})$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-10T17:13:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C12",
      "G.2.1",
      "G.2.2"
    ],
    "keywords": [
      "mixed metric dimension",
      "johnson graphs",
      "tight lower bound",
      "exact values",
      "hitting sets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}