{
  "abstract": "A set $D\\subseteq V(G)$ is a $1$-limited dominating set of a graph $G$ if every vertex outside $D$ has a neighbor in $D$ and every vertex of $D$ has at most one neighbor outside $D$. The minimum cardinality among all $1$-limited dominating sets of $G$ is denoted by $γ_1^{\\mathrm L}(G)$. For every cubic graph $G$ of order $n$, there exists a nonnegative integer $t$ such that $γ_1^{\\mathrm L}(G)=\\frac n2+t$. We establish structural properties of $1$-limited dominating sets in terms of $t$ and use them to study the induced cycles vertex number, that is, the maximum number of vertices inducing a $2$-regular subgraph. As applications, we determine the exact $1$-limited domination numbers of generalized Blanuša snarks and flower snarks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26259",
  "author_total": 3,
  "authors": [
    {
      "name": "Goran Radić"
    },
    {
      "name": "Gordana Radić"
    },
    {
      "name": "Aleksandra Tepeh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/an89rvq5tctvq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26259",
  "fulltext_url": null,
  "id": "an89rvq5tctvq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26259",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7223068087",
  "pdf_url": "https://arxiv.org/pdf/2610.26259",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/an89rvq5tctvq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.26259",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26259"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Structural aspects of $1$-limited domination in cubic graphs",
  "title_text": "Structural aspects of $1$-limited domination in cubic graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/an89rvq5tctvq",
  "venue": "arXiv",
  "versions": []
}