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Abstract A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S has an in-neighbor in S. A dominating set… Click to show full abstract
Abstract A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S has an in-neighbor in S. A dominating set S of D is called a total dominating set of D if the subdigraph induced by S has no isolated vertices. The total domination number of D, denoted by γt(D), is the minimum cardinality of a total dominating set of D. We show that for any connected digraph D of order n≥3, γt(D)+γt(D− )≤5n/3, where D− is the converse of D. Furthermore, we characterize the oriented trees for which the equality holds.
Keywords:
domination numbers;
converse;
total domination;
dominating set;
sum total
Journal Title: Quaestiones Mathematicae
Year Published: 2019
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Journal Title: Quaestiones Mathematicae
Year Published: 2019
Link to full text (if available)
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recommendations!