Geodesic
Spectral study of alliances in graphs
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 143-157

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In this paper we obtain several tight bounds on different types of alliance numbers of a graph, namely (global) defensive alliance number, global offensive alliance number and global dual alliance number. In particular, we investigate the relationship between the alliance numbers of a graph and its algebraic connectivity, its spectral radius, and its Laplacian spectral radius.
Keywords: defensive alliance, offensive alliance, dual alliance, domination, spectral radius, graph eigenvalues. 
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Rodríguez-Velazquez, Juan; Almira, Jose. Spectral study of alliances in graphs. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 143-157. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a12/