Geodesic
Fractional distance domination in graphs
Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 3, pp. 449-459

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Let G = (V,E) be a connected graph and let k be a positive integer with k ≤ rad(G). A subset D ⊆ V is called a distance k-dominating set of G if for every v ∈ V - D, there exists a vertex u ∈ D such that d(u,v) ≤ k. In this paper we study the fractional version of distance k-domination and related parameters.
Keywords: domination, distance k-domination, distance k-dominating function, k-packing, fractional distance k-domination 
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Arumugam, S.; Mathew, Varughese; Karuppasamy, K. Fractional distance domination in graphs. Discussiones Mathematicae. Graph Theory, Tome 32 (2012) no. 3, pp. 449-459. http://geodesic.mathdoc.fr/item/DMGT_2012_32_3_a5/