{
  "abstract": "Motivated by Brouwer's conjecture, Ashraf, Omidi and Tayfeh-Rezaie proposed the following Brouwer-type conjecture that for every graph $G$ on $n$ vertices with $m$ edges, the sum $S_k^+(G)$ of its $k$ largest signless Laplacian eigenvalues satisfies $S_k^+(G)\\le m+\\binom{k+1}{2}$ for $k=1, \\ldots, n$. In this paper, we prove that the above conjecture holds. Moreover, the equality holds if and only if $k=1$ and $G$ is either star $K_{1,a}$ or triangle $K_3$ with adding some isolated vertices. For split graphs, properties of block signless Laplacian matrices based on clique and independent set are adapted. While for non-split graphs, some spectral graph substructure are used to control the sum of signless Laplacian eigenvalues.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.31355",
  "author_total": 2,
  "authors": [
    {
      "name": "Ruisong Yuan"
    },
    {
      "name": "Xiao-Dong Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5jye1qztt1tsf.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.31355",
  "fulltext_url": null,
  "id": "5jye1qztt1tsf",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.31355",
  "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": "W7214610708",
  "pdf_url": "https://arxiv.org/pdf/2609.31355",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5jye1qztt1tsf.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.31355",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.31355"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Brouwer-type Conjecture for Signless Laplacian Eigenvalues of Graphs",
  "title_text": "On the Brouwer-type Conjecture for Signless Laplacian Eigenvalues of Graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/5jye1qztt1tsf",
  "venue": "arXiv",
  "versions": []
}