%0 Journal Article
%T The Italian domatic number of a digraph
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Volkmann, Lutz
%D 2019
%\ 06/01/2019
%V 4
%N 1
%P 61-70
%! The Italian domatic number of a digraph
%K Digraphs
%K Italian dominating function
%K Italian domination number
%K Italian domatic number
%R 10.22049/cco.2019.26360.1102
%X An Italian dominating function on a digraph $D$ with vertex set $V(D)$ is defined as a function $fcolon V(D)to {0, 1, 2}$ such that every vertex $vin V(D)$ with $f(v)=0$ has at least two in-neighbors assigned 1 under $f$ or one in-neighbor $w$ with $f(w)=2$. A set ${f_1,f_2,ldots,f_d}$ of distinct Italian dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vin V(D)$, is called an Italian dominating family (of functions) on $D$. The maximum number of functions in an Italian dominating family on $D$ is the Italian domatic number of $D$, denoted by $d_{I}(D)$. In this paper we initiate the study of the Italian domatic number in digraphs, and we present some sharp bounds for $d_{I}(D)$. In addition, we determine the Italian domatic number of some digraphs.
%U http://comb-opt.azaruniv.ac.ir/article_13845_b207051edc37d9a82ecd605da8ed79b4.pdf