Abstract
A function f defined on the vertices of a graph G = ( V , E ) , f : V → { - 1 , 0 , 1 } 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 γ t - ( G ) , of G is the minimum weight of a TMDF on G. In this paper, a sharp lower bound on γ t - of k-partite graphs is given.
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