italian domination in digraphs

if d=(v,a) be a finite and simple digraph, then an italian dominating function (idf) on a digraph d is a labeling f:v(d)→{0,1,2} such that for every vertex vєv with f(v)=0, either v has a in-neighbor with label 2, or v has least two in-neighbor with label 1. the weight of an italian dominating function f is the value w(f)=∑_vєv f(v). the italian domination number of a digraph d, denoted by γ_i(d), equals the minimum weight of an italian dominating function on d. in this paper we initate the study of italian dominating in digraphs and we present some bounds on γ_i(d)