A generalization of global dominating function

Let g be a graph‎. ‎a function f‎:‎v(g)⟶{0,1}‎, ‎satisfying‎ ‎the condition that every vertex u with f(u)=0 is adjacent with at‎ ‎least one vertex v such that f(v)=1‎, ‎is called a dominating function (df)‎. ‎the weight of f is defined as wet(f)=σv∈v(g)f(v)‎. ‎the minimum weight of a dominating function of g‎ ‎is denoted by‎ ‎γ(g)‎, ‎and is called the domination number of g‎. ‎a dominating‎ ‎function f is called a global dominating function (gdf) if f is‎ ‎also a df of g¯‎. ‎the minimum weight of a global dominating function is denoted by‎ ‎γg(g) and is called global domination number of g‎. ‎in this paper we introduce a generalization of global dominating function‎. ‎suppose g is a graph and s≥2 and kn is the complete graph on v(g)‎. ‎a function f:v(g)→{0,1} on g is s-dominating function (s−df)‎, ‎if there exists some factorization {g1,…,gs} of kn‎, ‎such that g1=g and f is dominating function of each gi‎.