Abstract The concept of the domination number plays an important role in both theory and applications of digraphs. Let D = ( V , A ) D=(V,A) be a digraph. A vertex subset T ⊆ V ( D ) T\subseteq V(D) is called a dominating set of D, if there is a vertex t ∈ T t\in T such that t v ∈ A ( D ) tv\in A(D) for every vertex v ∈ V ( D ) \ T v\in V(D)\backslash T . The dominating number of D is the cardinality of a smallest dominating set of D, denoted by γ ( D ) \gamma (D) . In this paper, the domination number of round digraphs is characterized completely.

中文翻译：

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圆有向图的支配数

摘要 支配数的概念在有向图的理论和应用中都占有重要地位。令 D = ( V , A ) D=(V,A) 是一个有向图。顶点子集 T ⊆ V ( D ) T\subseteq V(D) 称为 D 的支配集，如果存在顶点 t ∈ T t\in T 使得 tv ∈ A ( D ) tv\in A(D) ) 对于每个顶点 v ∈ V ( D ) \ T v\in V(D)\反斜杠 T 。D 的支配数是 D 的最小支配集的基数，用 γ ( D ) \gamma (D) 表示。本文完整地表征了圆有向图的支配数。