{
  "abstract": "Let $τ(G)$ denote the maximum number of edge-disjoint spanning trees in a connected graph $G$ of order $n$, and let $ρ_D(G)$ denote its distance spectral radius. For an integer $k\\ge2$, Fan, He and Zhao [Discrete Appl. Math. 376 (2025) 31--40] obtained a sharp distance spectral radius condition for $τ(G)\\ge k$ when $n\\ge2k+6$. In this paper, we fill the gap $2k\\le n\\le2k+5$ and thus complete the result for all $n\\ge2k$. The extremal graph given by Fan, He and Zhao remains valid for $n\\ge2k+2$, while we determine the unique extremal graph for each of the orders $n=2k$ and $n=2k+1$. We further obtain sharp distance spectral radius conditions and characterize all extremal graphs under the minimum degree condition $δ(G)\\ge k$ for all $n\\ge2k$. Finally, for graphs with the stronger minimum degree condition $δ(G)\\ge6k-4$ and order $n\\ge2δ(G)+2$, we obtain a sharp distance spectral radius condition ensuring $τ(G)\\ge k$ and determine the unique extremal graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25794",
  "author_total": 2,
  "authors": [
    {
      "name": "Yongbin Gao"
    },
    {
      "name": "Ligong Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b5e4332njm3cs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25794",
  "fulltext_url": null,
  "id": "b5e4332njm3cs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25794",
  "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": "W7214118186",
  "pdf_url": "https://arxiv.org/pdf/2609.25794",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b5e4332njm3cs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25794",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25794"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Some results on the distance spectral radius and edge-disjoint spanning trees of graphs",
  "title_text": "Some results on the distance spectral radius and edge-disjoint spanning trees of graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/b5e4332njm3cs",
  "venue": "arXiv",
  "versions": []
}