# On the out-domination and in-domination numbers of a digraph

- Authors
- Journal
- Discrete Mathematics 0012-365X
- Publisher
- Elsevier
- Publication Date
- Identifiers
- DOI: 10.1016/s0012-365x(99)90059-6
- Keywords

## Abstract

Abstract An out-domination set of a digraph D is a set S of vertices of D such that every vertex of D− S is adjacent from some vertex of S. The minimum cardinality of an out-domination set of D is the out-domination number γ +( D). The in-domination number γ −( D) is defined analogously. It is shown that for every digraph D of order n with no isolates, γ −( D)+ γ −( D) ⩽ 4 n/3. Furthermore, the digraphs D for which equality holds are characterized. Other inequalities are also derived.

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