Minus domination number in k-partite graphs

A function f de1ned 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∈V f(v). The minus domination number of a graph G, denoted by −(G), equals the minimum weight of a minus dominating function of G. In this paper, a sharp lower bound on − 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. c © 2003 Elsevier B.V. All rights reserved.