{
  "abstract": "We prove the conjecture of Xu, Li, Hua, and Pan that the resistance diameter does not increase under the line-graph operation. For every finite connected simple graph $G$ with at least one edge, we establish $D_r(L(G))\\le D_r(G)$, with equality if and only if $G$ is a cycle or $K_4$. The proof combines an exact electrical representation of $L(G)$ by stars with a sharp budget inequality for the branch core. This inequality controls the combined error terms arising from the comparison of degree-two paths and is central to both the diameter bound and the equality analysis.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.15133",
  "author_total": 3,
  "authors": [
    {
      "name": "Xiang-Feng Pan"
    },
    {
      "name": "Xiang-Yang Liu"
    },
    {
      "name": "Zhen-Mu Hong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2v5gnt2sdph8w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.15133",
  "fulltext_url": null,
  "id": "2v5gnt2sdph8w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.15133",
  "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.CO"
    ],
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7213297403",
  "pdf_url": "https://arxiv.org/pdf/2609.15133",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2v5gnt2sdph8w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.15133",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.15133"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "A proof of the resistance diameter conjecture for line graphs",
  "title_text": "A proof of the resistance diameter conjecture for line graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/2v5gnt2sdph8w",
  "venue": "arXiv",
  "versions": []
}