The geodesic transversal problem on some networks
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Publication:6378053
DOI10.1007/S40314-023-02199-9arXiv2109.09372MaRDI QIDQ6378053
Paul Manuel, B. Brešar, Sandi Klavžar
Publication date: 20 September 2021
Abstract: A set S of vertices of a graph G is a geodesic transversal of G if every maximal geodesic of G contains at least one vertex of S. We determine a smallest geodesic transversal in certain interconnection networks such as mesh of trees, and some well-known chemical structures such as silicate networks and carbon nanosheets. Some useful general bounds for the corresponding graph invariant are obtained along the way.
Small world graphs, complex networks (graph-theoretic aspects) (05C82) Distance in graphs (05C12) Transversal (matching) theory (05D15) Molecular structure (graph-theoretic methods, methods of differential topology, etc.) (92E10) Chemical graph theory (05C92)
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