{
  "abstract": "The generating graph $Γ(G)$ of a group $G$ is the graph whose vertex set is $G$, where two distinct vertices are adjacent if and only if they generate $G$. In this paper, we systematically study the structure of generating graphs of finite abelian groups (non-cyclic) and determine the set of all generating pairs. Moreover, we give some structural characterizations, in particular, we determine conditions under which $Γ(G)$ is regular, characterize when the isolated vertices form a subgroup, and establish necessary and sufficient conditions for two non-isomorphic finite abelian groups $G$ and $H$ to satisfy $Γ(G)\\cong Γ(H)$. Furthermore, we compute the spectra of the adjacency and Laplacian matrices of these graphs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00102",
  "author_total": 2,
  "authors": [
    {
      "name": "Kavita Samant"
    },
    {
      "name": "A. Satyanarayana Reddy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4c0b2yrek22d2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00102",
  "fulltext_url": null,
  "id": "4c0b2yrek22d2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00102",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7206156252",
  "pdf_url": "https://arxiv.org/pdf/2609.00102",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4c0b2yrek22d2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00102",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00102"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On the Generating Graph of Finite Abelian Groups",
  "title_text": "On the Generating Graph of Finite Abelian Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/4c0b2yrek22d2",
  "venue": "arXiv",
  "versions": []
}