{
  "abstract": "We say that a graph is resistance nonnegative or RN if it admits a positive edge-weight that yields nonnegative resistance curvature in the sense of Devriendt and Lambiotte. Analogously, a graph may be resistance positive or RP; we say a graph is strictly RN if it is RN but not RP. In this paper, we show that every $2$-connected strictly RN graph is bipartite with parts whose sizes differ by one, demonstrating that there are no $1$-tough strictly RN graphs. As a consequence, we prove that every $1$-tough RN graph is also RP. Lastly, we quantify the exact toughness values an RN graph can attain below $1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.23394",
  "author_total": 1,
  "authors": [
    {
      "name": "Hailey Jay Garcia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/213jsx9ngk628.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.23394",
  "fulltext_url": null,
  "id": "213jsx9ngk628",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.23394",
  "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": "W7214018464",
  "pdf_url": "https://arxiv.org/pdf/2609.23394",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/213jsx9ngk628.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.23394",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.23394"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Classification of strictly resistance nonnegative graphs",
  "title_text": "Classification of strictly resistance nonnegative graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/213jsx9ngk628",
  "venue": "arXiv",
  "versions": []
}