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Analogies between the geodetic number and the Steiner number of some classes of graphs

  • Identification data

    Identifier: imarina:5128966
  • Authors:

    Yero, Ismael G.
    Rodriguez-Velazquez, Juan A.
  • Others:

    Author, as appears in the article.: Yero, Ismael G.; Rodriguez-Velazquez, Juan A.;
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Rodríguez Velázquez, Juan Alberto
    Keywords: Steiner sets Geodetic sets Corona graph
    Abstract: A set of vertices S of a graph G is a geodetic set of G if every vertex v  S lies on a shortest path between two vertices of S. The minimum cardinality of a geodetic set of G is the geodetic number of G and it is denoted by 1(G). A Steiner set of G is a set of vertices W of G such that every vertex of G belongs to the set of vertices of a connected subgraph of minimum size containing the vertices of W. The minimum cardinality of a Steiner set of G is the Steiner number of G and it is denoted by s(G). Let G and H be two graphs and let n be the order of G. The corona product G ¿ H is defined as the graph obtained from G and H by taking one copy of G and n copies of H and joining by an edge each vertex from the ith-copy of H to the ith-vertex of G. We study the geodetic number and the Steiner number of corona product graphs. We show that if G is a connected graph of order n ≥ 2 and H is a non complete graph, then g(G ¿ H) ≤ s(G ¿ H), which partially solve the open problem presented in [Discrete Mathematics 280 (2004) 259-263] related to characterize families of graphs G satisfying that g(G) ≤ s(G).
    Thematic Areas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics Engenharias iii Economia Ciências agrárias i
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: juanalberto.rodriguez@urv.cat
    Author identifier: 0000-0002-9082-7647
    Record's date: 2023-11-18
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/858
    Papper original source: Filomat. 29 (8): 1781-1788
    APA: Yero, Ismael G.; Rodriguez-Velazquez, Juan A.; (2015). Analogies between the geodetic number and the Steiner number of some classes of graphs. Filomat, 29(8), 1781-1788. DOI: 10.2298/FIL1508781Y
    Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.2298/FIL1508781Y
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2015
    Publication Type: Journal Publications
  • Keywords:

    Mathematics,Mathematics (Miscellaneous),Mathematics, Applied
    Steiner sets
    Geodetic sets
    Corona graph
    Mathematics, applied
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    General mathematics
    Engenharias iii
    Economia
    Ciências agrárias i
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