{
  "abstract": "A geodesic $P$ of a connected graph $G(V,E)$ is called a maximal geodesic if there exists no geodesic $P'$ in $G$ that contains $P$ as its sub-path. The geodesic transversal problem determines a subset $S\\subseteq V(G)$ such that every possible maximal geodesic of $G$ includes at least one vertex of $S$. Such a set with minimum number of elements is called a gt-set and its cardinality is the gt-number of $G$. In this paper, we establish a general result, called the Geodesic Transversal lemma which provides a lower bound for the gt-number of an arbitrary graph $G$ in terms of the gt-number of its induced subgraphs. Using this lemma, we determine the gt-number of Butterfly and Hypercube networks.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06107",
  "author_total": 3,
  "authors": [
    {
      "name": "R. Prabha"
    },
    {
      "name": "B. Sandhiya"
    },
    {
      "name": "Paul Manuel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1dg92njvjy5qa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06107",
  "fulltext_url": null,
  "id": "1dg92njvjy5qa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06107",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06107",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1dg92njvjy5qa.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06107",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06107"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Geodesic Transversal of Hypercube and Butterfly networks",
  "title_text": "Geodesic Transversal of Hypercube and Butterfly networks",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/1dg92njvjy5qa",
  "venue": "arXiv",
  "versions": []
}