Geodesic
Upper signed k-domination number
Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 1, pp. 9-14 
S. Aram; S. M. Sheikholeslami; L. Volkmann; S. Aram; S. M. Sheikholeslami; L. Volkmann. Upper signed k-domination number. Acta mathematica Universitatis Comenianae, Tome 81 (2012) no. 1, pp. 9-14. http://geodesic.mathdoc.fr/item/AMUC_2012_81_1_a1/
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     author = {S. Aram and S. M. Sheikholeslami and L. Volkmann and S. Aram and S. M. Sheikholeslami and L. Volkmann},
     title = { Upper signed k-domination number},
     journal = {Acta mathematica Universitatis Comenianae},
     pages = {9--14},
     year = {2012},
     volume = {81},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2012_81_1_a1/}
}
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Voir la notice de l'article provenant de la source Comenius University

Let k 3 1 be an integer and let D = (V, A) be a finite simple digraph in which dD-(v) 3 k - 1 for all v Î V. A function f: V ® {-1,1} is called a signed k-dominating function (SkDF) if f(N-[v]) 3 k for each vertex v Î V. An SkDF f of a digraph D is minimal if there is no SkDF g 1 f such that g(v) £ f(v) for each v Î V. The maximum values of åv Î Vf(v), taken over all minimal signed k-dominating functions f, is called the upper signed k-domination number GkS(D). In this paper, we present a sharp upper bound for GkS(D).