Abstract
A function f defined on the vertices of a graph G=(V,E),f:V→{−1,0,1} is a minus dominating function if the sum of its values over any closed neighborhood is at least one. The weight of a minus dominating function is f(V)=∑v∈Vf(v). The minus domination number of a graph G, denoted by γ−(G), equals the minimum weight of a minus dominating function of G. In this paper, a sharp lower bound on γ− of k-partite graphs is given. The special case k=2 implies that a conjecture proposed by Dunbar et al. (Discrete Math. 199(1999) 35) is true.
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