Signed total domination numbers of directed graphs

Abstract

Let D = (V, A) be a finite simple directed graph (shortly digraph) in which d^-_D(v) > 1 for all v ε V. A function f : V → {-1,1} is called a signed total dominating function if f(N- (v)) > 1 for each vertex v ε; V. The signed total domination number for a digraph D is γ _st(D) = min{w(f) |f is a STDF of D}. In this paper, we initiate the study of signed total domination in digraphs and we present some sharp lower bounds for γ_st in terms of the order, the maximum degree and the chromatic number.