Abstract
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.
Highlights
The domination theory of graphs was derived from a board game in ancient India
In 1962, Ore formally gave the definitions of the dominating set and the domination number in [1]
The dominating number of D is the cardinality of a smallest dominating set of D, denoted by γ(D)
Summary
The domination theory of graphs was derived from a board game in ancient India. In 1962, Ore formally gave the definitions of the dominating set and the domination number in [1]. Domination in digraphs has not yet gained the same amount of attention, it has several useful applications as well It has been used in the study of answering skyline query in the database [3] and routing problems in networks [4]. Let D = (V, A) be a digraph, which means that V and A represent the vertex set and the arc set of D, respectively. The order of D is the number of vertices in D, denoted by |V(D)|. The digraph D is strongly connected (or strong) if, for each pair u and v of distinct vertices in D, there is a (u, v)-walk and a (v, u)-walk. The domination number of a round digraph is characterized by studying the round local tournament and the round non-local tournament, respectively
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