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

  • Datos identificativos

    Identificador: imarina:5128966
    Autores:
    Yero, Ismael GRodriguez-Velazquez, Juan A
    Resumen:
    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).
  • Otros:

    Autor según el artículo: Yero, Ismael G; Rodriguez-Velazquez, Juan A
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: Rodríguez Velázquez, Juan Alberto
    Palabras clave: Steiner sets Geodetic sets Corona graph
    Resumen: 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).
    Áreas temáticas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics Engenharias iii Economia Ciências agrárias i
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: juanalberto.rodriguez@urv.cat
    Identificador del autor: 0000-0002-9082-7647
    Fecha de alta del registro: 2024-10-26
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/858
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referencia al articulo segun fuente origial: Filomat. 29 (8): 1781-1788
    Referencia de l'ítem segons les normes 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
    DOI del artículo: 10.2298/FIL1508781Y
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2015
    Tipo de publicación: Journal Publications
  • Palabras clave:

    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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