{
  "abstract": "For a graph $G$, let $i_k(G)$ denote the number of independent sets of cardinality $k$, and let \\[ I(G,z)=\\sum_{k\\ge0} i_k(G)z^k \\] be its independence polynomial. Following Brown and Cameron \\cite{BrownCameron2018}, a graph is called stable if all zeros of its independence polynomial lie in the closed left half-plane. They proved that every star is stable, but also constructed nonstable trees. They then asked for a characterization of stable trees. In this paper, we extend and strengthen their result by proving that every spider, obtained from a star by arbitrary and possibly nonuniform subdivisions of its edges, has all its independence roots in the open left half-plane. Hence, every spider is stable.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04694",
  "author_total": 2,
  "authors": [
    {
      "name": "Lei Zhang"
    },
    {
      "name": "Jianhua Tu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f7n5t7ne8tnek.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04694",
  "fulltext_url": null,
  "id": "f7n5t7ne8tnek",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04694",
  "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.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7211878061",
  "pdf_url": "https://arxiv.org/pdf/2609.04694",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f7n5t7ne8tnek.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04694",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04694"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Stability of independence polynomials of spiders",
  "title_text": "Stability of independence polynomials of spiders",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/f7n5t7ne8tnek",
  "venue": "arXiv",
  "versions": []
}