{
  "abstract": "The weakly zero-divisor graph $WΓ(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$, and two distinct vertices $x$, $y$ are adjacent if and only if there exists $w\\in {\\rm ann}(x)$ and $ z\\in {\\rm ann}(y)$ such that $wz =0$. In this paper, first we prove that the vertex connectivity of $WΓ(R)$ is equal to its minimum degree, where $R$ is either an Artinian ring or reduced ring. For any finite ring $R$, we obtain the vertex connectivity of $WΓ(R)$. Moreover, this paper characterizes all the vertices that attain the minimum degree of $WΓ(R)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02103",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohd Shariq"
    },
    {
      "name": "Jitender Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/23mabyagnvpev.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02103",
  "fulltext_url": null,
  "id": "23mabyagnvpev",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02103",
  "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|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7207535392",
  "pdf_url": "https://arxiv.org/pdf/2609.02103",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/23mabyagnvpev.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.02103",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02103"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the vertex connectivity of weakly zero-divisor graph of commutative rings",
  "title_text": "On the vertex connectivity of weakly zero-divisor graph of commutative rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/23mabyagnvpev",
  "venue": "arXiv",
  "versions": []
}