Articles producció científica> Enginyeria Informàtica i Matemàtiques

Boundary powerful k-alliances in graphs

  • Identification data

    Identifier: PC:513
    Handle: https://hdl.handle.net/20.500.11797/PC513
    Authors:
    Rodriguez-Velazquez, J.A.Yero, I.G.
    Abstract:
    A global boundary defensive k-alliance in a graph G = (V, E) is a dominating set S of vertices of G with the property that every vertex in 5 has fc more neighbors in 5 than it has outside of S. A global boundary offensive fc-alliance in a graph G is a set S of vertices of G with the property that every vertex in V - S has fc more neighbors in S than it has outside of S. We define a global boundary powerful fc-alliance as a set 5 of vertices of G, which is both global boundary defensive kalliance and global boundary offensive (k + 2)-alliance. In this paper we study mathematical properties of boundary powerful k-alliances. In particular, we obtain several bounds (closed formulas for the case of regular graphs) on the cardinality of every global boundary powerful k-alliance. In addition, we consider the case in which the vertex set of a graph G can be partitioned' into two boundary powerful fcalliances, showing that, in such a case, k = - 1 and, if G is amp;d-regular, its algebraic connectivity is equal to amp;d +1.

  • Others:

    Author, as appears in the article.: Rodriguez-Velazquez, J.A. Yero, I.G.
    Papper version: info:eu-repo/semantics/acceptedVersion
    Department: Enginyeria Informàtica i Matemàtiques
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Abstract: A global boundary defensive k-alliance in a graph G = (V, E) is a dominating set S of vertices of G with the property that every vertex in 5 has fc more neighbors in 5 than it has outside of S. A global boundary offensive fc-alliance in a graph G is a set S of vertices of G with the property that every vertex in V - S has fc more neighbors in S than it has outside of S. We define a global boundary powerful fc-alliance as a set 5 of vertices of G, which is both global boundary defensive kalliance and global boundary offensive (k + 2)-alliance. In this paper we study mathematical properties of boundary powerful k-alliances. In particular, we obtain several bounds (closed formulas for the case of regular graphs) on the cardinality of every global boundary powerful k-alliance. In addition, we consider the case in which the vertex set of a graph G can be partitioned' into two boundary powerful fcalliances, showing that, in such a case, k = - 1 and, if G is amp;d-regular, its algebraic connectivity is equal to amp;d +1.
    Entity: Universitat Rovira i Virgili.
    Journal publication year: 2013
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 0381-7032
    First page: 495
    Last page: 505
    Journal volume: 111