{
  "abstract": "Let $T_{m,n}$ be the tadpole graph obtained by joining a cycle $C_m$ to a path $P_n$ by a bridge. We prove that the independence polynomial of every tadpole graph is unimodal and establish sharp bounds for its mode. The unimodality result follows from a general criterion for graphs obtained by attaching a path to a fixed vertex. Over a field of characteristic zero, we also give a complete classification of the pairs $(m,n)$ for which the Artinian algebra defined by the edge ideal of $T_{m,n}$ together with the squares of all variables has the weak Lefschetz property.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13888",
  "author_total": 3,
  "authors": [
    {
      "name": "Tran Quang Hoa"
    },
    {
      "name": "Nguyen Duy Phuoc"
    },
    {
      "name": "Tran Nguyen Thanh Son"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6ae5jxvjzkyhn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13888",
  "fulltext_url": null,
  "id": "6ae5jxvjzkyhn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13888",
  "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.AC"
    ],
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2602|Commutative Algebra and Its Applications"
    ]
  ],
  "openalex": "W7213247923",
  "pdf_url": "https://arxiv.org/pdf/2609.13888",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ae5jxvjzkyhn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.13888",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13888"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Independence polynomials and the weak Lefschetz property for tadpole graphs",
  "title_text": "Independence polynomials and the weak Lefschetz property for tadpole graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/6ae5jxvjzkyhn",
  "venue": "arXiv",
  "versions": []
}