{
  "abstract": "For a given connected graph $G(V,E)$, the geodesic transversal problem finds a set $S$ of vertices of $G$ with minimum cardinality such that every maximal geodesic of $G$ contains at least one vertex of $S$. The cardinality of such a smallest set $S$ is called the gt-number of $G$ and is denoted as $gt(G)$. In this paper, we introduce the \\textit{Edge geodesic transversal problem} as the edge-based extension of the geodesic transversal problem. The problem of determining a set $S\\subseteq E(G)$ with minimum number of elements such that every maximal geodesic $P$ in $G$ traverses at least one edge of $S$ is called the edge geodesic transversal problem, and the cardinality of such a set is called the edge geodesic transversal number or the $gt_e$-number of $G$, denoted as $gt_e(G)$. Further, we investigate the effect of an edge cut of a graph on the edge geodesic transversal problem and prove a novel result called the edge cut transversal theorem which is used in the computation of edge geodesic transversal number of hypercube, stacked prism and ladder graph.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36821",
  "author_total": 3,
  "authors": [
    {
      "name": "R. Prabha"
    },
    {
      "name": "B. Sandhiya"
    },
    {
      "name": "Paul Manuel"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/83kzrzjhhe1m5.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36821",
  "fulltext_url": null,
  "id": "83kzrzjhhe1m5",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36821",
  "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"
    ],
    [
      "openalex",
      "1703|Advanced Graph Theory Research"
    ]
  ],
  "openalex": "W7224132074",
  "pdf_url": "https://arxiv.org/pdf/2610.36821",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/83kzrzjhhe1m5.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.36821",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36821"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "The Edge Geodesic Transversal Problem",
  "title_text": "The Edge Geodesic Transversal Problem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/83kzrzjhhe1m5",
  "venue": "arXiv",
  "versions": []
}