The domination number of round digraphs

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∈Tt\in T such that tv∈A(D)tv\in A(D) for every vertex v∈V(D)\Tv\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.

Keywords

• domination number
• round digraph
• local tournament
• purely local tournament
• 05c69