{
  "abstract": "Given a graph $G$, a set $W$ of vertices of $G$ is a resolving set if, for any pair of vertices $z_1$ and $z_2$ of $G$, there is a vertex $w\\in W$ such that $d(w,z_1)\\ne d(w,z_2)$, where $d(u,v)$ denotes the length of a shortest path between the vertices $u$ and $v$. The metric dimension of a graph $G$, $β(G)$, is the minimum cardinality of a resolving set of $G$. A resolving set $W$ is fault-tolerant if $W\\setminus \\{w\\}$ is a resolving set for any $w\\in W$. The fault-tolerant metric dimension of a graph $G$, denoted by $β'(G)$, is the minimum cardinality of a fault-tolerant resolving set of $G$. In this paper, we study the fault-tolerant metric dimension problem in maximal outerplanar graphs. In particular, we show that there are exactly two maximal outerplanar graphs with $β'(G)=3$. We also show that $4\\le β'(G) \\le 6$ for any maximal outerplanar graph $G$ of order at least 7 and metric dimension 2. Moreover, we establish the upper bound $β'(G) \\le \\left\\lceil \\frac{2n}{3} \\right\\rceil$ for maximal outerplanar graphs $G$ of order $n\\ge 5$, by building in linear time a fault-tolerant resolving set of cardinality $\\left\\lceil \\frac{2n}{3} \\right\\rceil$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13374",
  "author_total": 4,
  "authors": [
    {
      "name": "Carmen Hernando"
    },
    {
      "name": "Montserrat Maureso"
    },
    {
      "name": "Mercè Mora"
    },
    {
      "name": "Javier Tejel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8nwyhns7h48vv.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13374",
  "fulltext_url": null,
  "id": "8nwyhns7h48vv",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13374",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7221514645",
  "pdf_url": "https://arxiv.org/pdf/2610.13374",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8nwyhns7h48vv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13374",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13374"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the fault-tolerant metric dimension of maximal outerplanar graphs",
  "title_text": "On the fault-tolerant metric dimension of maximal outerplanar graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/8nwyhns7h48vv",
  "venue": "arXiv",
  "versions": []
}