Geodesic
On the Signed (Total) k-Independence Number in Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 651-662

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Let G be a graph. A function f : V (G) → −1, 1 is a signed k- independence function if the sum of its function values over any closed neighborhood is at most k − 1, where k ≥ 2. The signed k-independence number of G is the maximum weight of a signed k-independence function of G. Similarly, the signed total k-independence number of G is the maximum weight of a signed total k-independence function of G. In this paper, we present new bounds on these two parameters which improve some existing bounds.
Keywords: domination in graphs, signed k-independence, limited packing, tuple domination 
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Khodkar, Abdollah; Samadi, Babak; Volkmann, Lutz. On the Signed (Total) k-Independence Number in Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 651-662. http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a4/