{
  "abstract": "Two graphs are degree similar if their adjacency matrices and their degree matrices are simultaneously similar, a notion recently introduced by Godsil and Sun. We extend it to signed graphs in two ways, degree similarity and net-degree similarity, according to whether the degree or the net-degree matrix is used. We prove that signed trees are determined by their degree similarity class, but not by their net-degree similarity class. We then develop constructions of (net-)degree similar signed graphs, based on a signed version of Godsil--McKay switching, on partial transposition and on block extensions. As a byproduct, we obtain infinite families both of pairs of net-degree similar unicyclic signed graphs with non-isomorphic underlying graphs, and of unicyclic signed graphs, not necessarily regular, which are not determined by their degree similarity class. This settles the net-degree version of a problem of Godsil and Sun on unicyclic graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.13863",
  "author_total": 2,
  "authors": [
    {
      "name": "Matteo Cavaleri"
    },
    {
      "name": "Alfredo Donno"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7kghd6adjwvj4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.13863",
  "fulltext_url": null,
  "id": "7kghd6adjwvj4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.13863",
  "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": "W7221550110",
  "pdf_url": "https://arxiv.org/pdf/2610.13863",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7kghd6adjwvj4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.13863",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.13863"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Degree similar and net-degree similar signed graphs",
  "title_text": "Degree similar and net-degree similar signed graphs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/7kghd6adjwvj4",
  "venue": "arXiv",
  "versions": []
}