{
  "abstract": "The Sombor index of a graph G is SO(G)=∑uv∈E(G)(dG(u)2+dG(v)2)1/2, where dG(v) denotes the degree of v. The repetition number of G is the maximum multiplicity of an entry in its degree sequence. In this paper, we determine the maximum Sombor index among connected graphs with given repetition number r and cyclomatic number c, where c≥1 and r≥max{3,2c}. We characterize all graphs attaining the maximum value of the Sombor index. These extremal graphs consist of c cycles sharing one common vertex, together with r pendant vertices adjacent to the common vertex. For graphs outside the extremal family, we establish an explicit upper bound smaller than the maximum value. When r≥2c+1, we characterize all graphs attaining this bound, which also yields the second largest Sombor index. If r=2c, the bound is strict. We further prove a general lower bound in terms of the repetition number and a stronger bound involving both r and c for graphs with positive cyclomatic number. For c=1, the lower and upper bounds are both sharp for unicyclic graphs with given repetition number.",
  "abstract_shown": true,
  "affiliations": [
    "Faculty of Mathematics and Physics, Huai’an University, Huai’an 223003, China"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Hongbo Hua",
      "orcid": "0000-0001-7152-466X"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/be71cd5pkwnz0.bib",
  "cited_by": 0,
  "doi": "10.3390/axioms15100757",
  "fulltext_url": null,
  "id": "be71cd5pkwnz0",
  "issns": [
    "2075-1680"
  ],
  "landing_url": "https://www.mdpi.com/2075-1680/15/10/757",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2608|Graph theory and applications"
    ]
  ],
  "openalex": "W7221526631",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-10",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/be71cd5pkwnz0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:30Z",
      "native_id": "10.3390/axioms15100757",
      "source": "crossref",
      "url": "https://www.mdpi.com/2075-1680/15/10/757"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2608|Graph theory and applications",
      "subfield": "geometry-topology"
    }
  ],
  "title": "The Sombor Index of Connected Graphs with Given Repetition Number and Cyclomatic Number",
  "title_text": "The Sombor Index of Connected Graphs with Given Repetition Number and Cyclomatic Number",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:30Z",
  "url": "https://research.draconitic.com/paper/be71cd5pkwnz0",
  "venue": "Axioms",
  "versions": []
}