Author, as appears in the article.: Rodriguez-Velazquez, J.A. Yero, I.G.
Department: Enginyeria Informàtica i Matemàtiques
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.
licence for use: https://creativecommons.org/licenses/by/3.0/es/
ISSN: 0381-7032
Last page: 505
Journal volume: 111
Papper version: info:eu-repo/semantics/acceptedVersion
Link to the original source: http://combinatorialmath.ca/ArsCombinatoria/Vol111.html
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Entity: Universitat Rovira i Virgili.
Journal publication year: 2013
First page: 495