ON SIGNED ARC TOTAL DOMINATION IN DIGRAPHS

Let D = (V, A) be a finite simple digraph and N(uv) = {u'v' not equal uv vertical bar u = u' or v = v'} be the open neighbourhood of uv in D. A function f : A -> {-1, +1} is said to be a signed arc total dominating function (SATDF) of D if Sigma(e'is an element of N(uv)) f(e') >= 1 holds for every arc uv is an element of A. The signed arc total domination number gamma(st)'(D) is defined as gamma(st)'(D) = min{Sigma(e is an element of A) f(e) vertical bar f is an SATDF of D}. In this paper we initiate the study of the signed arc total domination in digraphs and present some lower bounds for this parameter.