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A Generalization Of Global Dominating Function

M. Momeni, A. Zaeembashi
Published 2019 · Mathematics

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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.
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