TWIN MINUS TOTAL DOMINATION NUMBERS IN DIRECTED GRAPHS

Let D = (V, A) be a finite simple directed graph (shortly, digraph). A function f :V -> {-1, 0, 1} is called a twin minus total dominating function (TMTDF) if f (N- (v)) >= 1 and f (N+ (v)) >= 1 for each vertex v is an element of V. The twin minus total domination number of D is gamma*(mt) (D) = min{w(f) f is a TMTDF of D}. In this paper, we initiate the study of twin minus total domination numbers in digraphs and we present some lower bounds for gamma*(mt) (D) in terms of the order, size and maximum and minimum in-degrees and out-degrees. In addition, we determine the twin minus total domination numbers of some classes of digraphs.