{
  "abstract": "Rashidi, Shajareh Poursalavati, and Tavakkoli [J. Algebra Comb. Discrete Struct. Appl. 7 (2020), no.2, 183-193, Theorem 3.6] claim $Z(P(n,3)) = 8$ for all $n \\geq 12$, but this fails at $n = 12$, where $Z(P(12,3)) = 7$. We give an explicit $7$-vertex zero forcing set for $P(12,3)$ and its forcing sequence, and verify by exhaustive search that no $6$-vertex set forces $P(12,3)$. We prove $Z(P(n,3)) \\le 8$ for $n \\ge 9$ using an explicit forcing set and rotational symmetry. Exhaustive search yields $Z(P(n,3))$ for $7 \\le n \\le 20$ and identifies the gap in the published proof: its case analysis fails to exclude $7$-vertex sets. We conjecture $Z(P(n,3)) = 8$ for $n \\ge 13$, requiring a matching lower bound for all large $n$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.19412",
  "author_total": 1,
  "authors": [
    {
      "name": "Arnav Krishnan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d2270rtm96n4k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.19412",
  "fulltext_url": null,
  "id": "d2270rtm96n4k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.19412",
  "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|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7170166251",
  "pdf_url": "https://arxiv.org/pdf/2607.19412",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d2270rtm96n4k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2607.19412",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.19412"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A correction to the Zero Forcing Number of the Generalized Petersen Graphs $P(n,3)$",
  "title_text": "A correction to the Zero Forcing Number of the Generalized Petersen Graphs P(n,3)",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/d2270rtm96n4k",
  "venue": "arXiv",
  "versions": []
}