On the complement graph and defensive k-alliances

Authors:
J. M. Sigarreta;S. Bermudo;H. Fernau
Affiliations:
Faculty of Mathematics, Autonomous University of Guerrero. Carlos E. Adame 5, Col. La Garita, Acapulco, Guerrero, Mexico;Department of Economy, Quantitative Methods and Economic History, Pablo de Olavide University. Carretera de Utrera Km. 1, 41013-Sevilla, Spain;Fachbereich 4-Abteilung Informatik, Universität Trier, D-54286 Trier, Germany
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

In this paper, we obtain several tight bounds of the defensive k-alliance number in the complement graph from other parameters of the graph. In particular, we investigate the relationship between the alliance numbers of the complement graph and the minimum and maximum degree, the domination number and the isoperimetric number of the graph. Moreover, we prove the NP-completeness of the decision problem underlying the defensive k-alliance number.