{
  "abstract": "We give a combinatorial characterization of the $\\rm{v}$-number of a $t$-closed neighborhood ideal associated to a graph $G$, and investigate its relation with other invariants such as the $t$-domination number and the smallest size of a ball of radius $t$ in the graph $G$. We present several new cases where it is satisfied that the $\\rm{v}$-number is bounded above by the Castelnuovo-Mumford regularity. We analyze the behavior of the $\\rm{v}$-number of a $t$-closed neighborhood ideal with respect to the parameter $t$. Lastly, we compute explicit formulas for the $\\rm{v}$-number in the case of paths, cycles, and caterpillars, and analyze the case of Hamming graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.33858",
  "author_total": 4,
  "authors": [
    {
      "name": "Delio Jaramillo-Velez"
    },
    {
      "name": "Hiram H. López"
    },
    {
      "name": "Rodrigo San-José"
    },
    {
      "name": "Nart Shalqini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79kagy8jkz45d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.33858",
  "fulltext_url": null,
  "id": "79kagy8jkz45d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.33858",
  "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.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7223921221",
  "pdf_url": "https://arxiv.org/pdf/2610.33858",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79kagy8jkz45d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.33858",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.33858"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The $\\rm{v}$-number of $t$-closed neighborhood ideals",
  "title_text": "The v-number of t-closed neighborhood ideals",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/79kagy8jkz45d",
  "venue": "arXiv",
  "versions": []
}