{
  "abstract": "For a graph G=(V,E), a function f:V⟶{0,1,2} is a vertex–edge Roman {2}-dominating function (veR2DF) if for every edge xy∈E, either f(x)+f(y)≥1 or ∑z∈N(x)∪N(y)f(z)≥2. The sum ∑v∈Vf(v) is the weight of the function f. The vertex–edge Roman {2}-domination number of G, denoted by γveR2(G), is the minimum weight of a veR2DF of G. In this paper, we prove that for any connected graph G of order n≥4, then γveR2(G)≤n2, and this result is sharp. We also prove Nordhaus–Gaddum inequalities for γveR2(G). In addition, we characterize trees with equal vertex–edge Roman {2}-domination, vertex–edge domination, and domination numbers.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematics and Statistics, College of Science, King Faisal University, Al-Ahsa 31982, Saudi Arabia"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Ahlam Almulhim",
      "orcid": "0000-0001-9131-044X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1jzsgprf8dknd.bib",
  "cited_by": 0,
  "doi": "10.3390/math14203819",
  "fulltext_url": null,
  "id": "1jzsgprf8dknd",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/20/3819",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7222993874",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/1jzsgprf8dknd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14203819",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/20/3819"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "issn:2227-7390",
      "subfield": "general"
    }
  ],
  "title": "Graphs with Large Vertex–Edge Roman {2}-Domination Number",
  "title_text": "Graphs with Large Vertex–Edge Roman {2}-Domination Number",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/1jzsgprf8dknd",
  "venue": "Mathematics",
  "versions": []
}