Majority out-dominating sets in digraphs

The concept of majority domination in graphs has been defined in at least two different ways: As a function and as a set. In this work we extend the latter concept to digraphs, while the former was extended in another paper. Given a digraph \(D=(V,A),\) a set \(S\subseteq V\) is a \textit{majority o...

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Bibliographic Details
Published in:arXiv.org 2013-11
Main Authors: Ebadi, Karam, Manrique, Martín, Jafary, Reza, Manora, J Joseline
Format: Article
Language:English
Subjects:
Graph theory
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Summary:The concept of majority domination in graphs has been defined in at least two different ways: As a function and as a set. In this work we extend the latter concept to digraphs, while the former was extended in another paper. Given a digraph \(D=(V,A),\) a set \(S\subseteq V\) is a \textit{majority out-dominating set} (MODS) of \(D\) if \(|N^+[S]|\geq \frac {n}{2}.\) The minimum cardinality of a MODS in \(D\) is the {\it set majority out-domination number} \(\gamma^+_{m}(D)\) of \(D.\) In this work we introduce these concepts and prove some results about them, among which the characterization of minimal MODSs.
ISSN:2331-8422