A GENERALIZATION OF GLOBAL DOMINATING FUNCTION

Let G be a graph. A function f : V (G) -! f0; 1g, 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 dened as wet(f) = v2V (G)f(v). The minimum weight of a dominating function of G is denoted by (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 g(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) -! f0; 1g on G is s-dominating function (s - DF), if there exists some factorization fG1; : : : ;Gsg of Kn, such that G1 = G and f is dominating function of each Gi.