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