{
  "abstract": "The reduced power graph $Γ_{RP}(G)$ of a group $G$ is a simple graph with vertex set $G$, where two distinct vertices $u$ and $v$ are adjacent if and only if $\\langle u \\rangle \\subset \\langle v \\rangle$ or $\\langle v \\rangle \\subset \\langle u \\rangle$. An $L(2,1)$-labeling of a graph $Γ$ is a mapping from the vertex set of $Γ$ to the set of non-negative integers such that the labels of adjacent vertices differ by at least $2$ and the labels of vertices at distance two are distinct. The lambda number of $Γ$, denoted by $λ(Γ)$, is defined as the minimum possible span of labels among all $L(2,1)$-labelings of $Γ$. In this paper, we establish upper and lower bounds for $λ(Γ_{RP}(G))$ and characterize the conditions under which these bounds are achieved. As an application, we determine the exact value of $λ(Γ_{RP}(G))$ for certain classes of finite groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.25028",
  "author_total": 3,
  "authors": [
    {
      "name": "Siddharth Malviy"
    },
    {
      "name": "Keerttiranjan Sahoo"
    },
    {
      "name": "Vipul Kakkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/by4emzjcpkdse.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.25028",
  "fulltext_url": null,
  "id": "by4emzjcpkdse",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.25028",
  "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"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "1703|Graph Labeling and Dimension Problems"
    ]
  ],
  "openalex": "W7223014777",
  "pdf_url": "https://arxiv.org/pdf/2610.25028",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/by4emzjcpkdse.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2610.25028",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.25028"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Lambda number of the reduced power graph of finite groups",
  "title_text": "Lambda number of the reduced power graph of finite groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/by4emzjcpkdse",
  "venue": "arXiv",
  "versions": []
}