In this paper we introduced the concepts of global domination number and domatic in product fuzzy graph is denoted by γg(G) dg(G), respectively determine for several classes obtain Nordhaus-Gaddum type results parameter. Further, some bounds dg(G) are investigated. Also relations between γg(G)(dg(G)) other known parameter Product graphs Finally introduce concept full about done.

An {em 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-neighborsassigned 1 under $f$ or one in-neighbor $w$ with $f(w)=2$. A set ${f_1,f_2,ldots,f_d}$ of distinctItalian dominating functions on $D$ with the property that $sum_{i=1}^d f_i(v)le 2$ for each $vi...