Geodesic
Fractional global domination in graphs
Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 33-44

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Let G = (V,E) be a graph. A function g:V → [0,1] is called a global dominating function (GDF) of G, if for every v ∈ V, g(N[v]) = ∑_u ∈ N[v]g(u) ≥ 1 and g(N(v)) = ∑_u ∉ N(v)g(u) ≥ 1. A GDF g of a graph G is called minimal (MGDF) if for all functions f:V → [0,1] such that f ≤ g and f(v) ≠ g(v) for at least one v ∈ V, f is not a GDF. The fractional global domination number γ_fg(G) is defined as follows: γ_fg(G) = min|g|:g is an MGDF of G where |g| = ∑_v ∈ V g(v). In this paper we initiate a study of this parameter.
Keywords: domination, global domination, dominating function, global dominating function, fractional global domination number 
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Arumugam, Subramanian; Karuppasamy, Kalimuthu; Hamid, Ismail. Fractional global domination in graphs. Discussiones Mathematicae. Graph Theory, Tome 30 (2010) no. 1, pp. 33-44. http://geodesic.mathdoc.fr/item/DMGT_2010_30_1_a2/