Global defensive k-alliances in graphs

Authors:
J. A. Rodríguez-Velázquez;J. M. Sigarreta
Affiliations:
Department of Computer Engineering and Mathematics, Rovira i Virgili University of Tarragona, Av. Països Catalans 26, 43007 Tarragona, Spain;Departamento de Matemáticas, Universidad Carlos III de Madrid, Avda. de la Universidad 30, 28911 Leganés (Madrid), Spain
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 2
Cited 3

Algorithms and complexity for alliances and weighted alliances of various types

Algorithms and complexity for alliances and weighted alliances of various types
On the global offensive alliance number of a graph

Discrete Applied Mathematics

On the complement graph and defensive k-alliances

Discrete Applied Mathematics
Boundary defensive k-alliances in graphs

Discrete Applied Mathematics
Partitioning a graph into offensive k-alliances

Discrete Applied Mathematics

Quantified Score

Hi-index	0.04

Visualization

Abstract

Let @C=(V,E) be a simple graph. For a nonempty set X@?V, and a vertex v@?V, @d"X(v) denotes the number of neighbors v has in X. A nonempty set S@?V is a defensivek-alliance in @C=(V,E) if @d"S(v)=@d"S"@?(v)+k,@?v@?S. A defensive k-alliance S is called global if it forms a dominating set. The global defensivek-alliance number of @C, denoted by @c"k^a(@C), is the minimum cardinality of a defensive k-alliance in @C. We study the mathematical properties of @c"k^a(@C).