Total minus domination in k-partite graphs

A function f defined on the vertices of a graph image is a total minus dominating function (TMDF) if the sum of its values over any open neighborhood is at least one. The weight of a TMDF is the sum of its function values over all vertices. The total minus domination number, denoted by image, of G is the minimum weight of a TMDF on G. In this paper, a sharp lower bound on image of k-partite graphs is given.