{
  "abstract": "Let $μ(G)$ and $q(G)$ be the Laplacian and signless Laplacian spectral radii of a graph $G$. Li, Wang and Guo (2026) conjectured that, if $H$ with $|V(H)|\\geq 1$ is an induced subgraph of a graph $G$, then $μ(G)\\le\\max\\limits_{v\\in V(H)}μ(H_v^t)$ and $q(G)\\le\\max\\limits_{v\\in V(H)}q(H_v^t)$, where $t=e(G)-e(H)$ and $H_v^t$ is the graph obtained from $H$ by adding $t$ pendant edges to $v\\in V(H)$. We prove this conjecture by establishing a spectral comparison theorem for a broader family of positive semidefinite graph matrices which includes the Laplacian and signless Laplacian matrices. We also characterize all equality cases for the prescribed subgraph $H$ with $e(H)\\geq 1$ and $t\\geq 1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29048",
  "author_total": 3,
  "authors": [
    {
      "name": "Hongzhang Chen"
    },
    {
      "name": "Jianxi Li"
    },
    {
      "name": "Xiaoyun Lv"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hv0j0x3f1ca7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29048",
  "fulltext_url": null,
  "id": "8hv0j0x3f1ca7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29048",
  "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": "W7223223441",
  "pdf_url": "https://arxiv.org/pdf/2610.29048",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hv0j0x3f1ca7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.29048",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29048"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Proofs of Li, Wang and Guo's conjectures on (signless) Laplacian spectral radius",
  "title_text": "Proofs of Li, Wang and Guo's conjectures on (signless) Laplacian spectral radius",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/8hv0j0x3f1ca7",
  "venue": "arXiv",
  "versions": []
}