The Edge Geodesic Transversal Problem

@misc{prabha2026edge,
  title = {{The Edge Geodesic Transversal Problem}},
  author = {R. Prabha and B. Sandhiya and Paul Manuel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.36821},
  eprint = {2610.36821},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.36821},
  note = {CC0},
}

TY  - UNPB
TI  - The Edge Geodesic Transversal Problem
AU  - R. Prabha
AU  - B. Sandhiya
AU  - Paul Manuel
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.36821
UR  - https://arxiv.org/abs/2610.36821
AB  - 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⊆ 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.
ER  -