{
  "abstract": "The power graph of a finite group $G$ is a simple undirected graph with vertex set $G$ and two vertices are adjacent if one is a power of the other. The intersection power graph of a finite group $G$ is a simple undirected graph with vertex set $G$ and two vertices $x$, $y$ are adjacent if $\\langle x\\rangle \\cap \\langle y \\rangle \\neq \\{e\\}$. The difference graph $\\mathcal{D}(G)$ of a finite group $G$ is the difference of the intersection power graph and power graph with all isolated vertices removed. We characterized all the finite nilpotent groups $G$ except $2$-group such that the difference graph is planar. Further, we determine all the finite nilpotent groups whose difference graph has genus at most $2$. Moreover, we prove that there does not exist any finite group whose difference graph is projective planar.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.02945",
  "author_total": 3,
  "authors": [
    {
      "name": "Manisha"
    },
    {
      "name": "Ekta"
    },
    {
      "name": "Jitender Kumar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4d0mqvq39c5gd.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.02945",
  "fulltext_url": null,
  "id": "4d0mqvq39c5gd",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.02945",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7208725378",
  "pdf_url": "https://arxiv.org/pdf/2609.02945",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d0mqvq39c5gd.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2609.02945",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.02945"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "On embeddings of the difference graph of the intersection power graph and the power graph",
  "title_text": "On embeddings of the difference graph of the intersection power graph and the power graph",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/4d0mqvq39c5gd",
  "venue": "arXiv",
  "versions": []
}