DOMINATION AND EDGE DOMINATION IN TREES

Let \(G=(V,E)\) be a simple graph. A set \(S\subseteq V\) is a dominating set if every vertex in \(V \setminus S\) is adjacent to a vertex in \(S\). The domination number of a graph \(G\), denoted by \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\). A set \(D \subseteq E\) is an...

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Main Authors: B. Senthilkumar, Yanamandram B. Venkatakrishnan, H. Naresh Kumar
Format: Article
Language:English
Published: Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics 2020-07-01
Series:Ural Mathematical Journal
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Online Access:https://umjuran.ru/index.php/umj/article/view/223
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author B. Senthilkumar
Yanamandram B. Venkatakrishnan
H. Naresh Kumar
author_facet B. Senthilkumar
Yanamandram B. Venkatakrishnan
H. Naresh Kumar
author_sort B. Senthilkumar
collection DOAJ
description Let \(G=(V,E)\) be a simple graph. A set \(S\subseteq V\) is a dominating set if every vertex in \(V \setminus S\) is adjacent to a vertex in \(S\). The domination number of a graph \(G\), denoted by \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\). A set \(D \subseteq E\) is an edge dominating set if every edge in \(E\setminus D\) is adjacent to an edge in \(D\). The edge domination number of a graph \(G\), denoted by \(\gamma'(G)\) is the minimum cardinality of an edge dominating set of \(G\). We characterize trees with  domination number equal to twice edge domination number.
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institution Kabale University
issn 2414-3952
language English
publishDate 2020-07-01
publisher Ural Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and Mechanics
record_format Article
series Ural Mathematical Journal
spelling doaj-art-ee03f48e4bc445eaba1a2864dca43cbf2025-08-20T03:57:55ZengUral Branch of the Russian Academy of Sciences and Ural Federal University named after the first President of Russia B.N.Yeltsin, Krasovskii Institute of Mathematics and MechanicsUral Mathematical Journal2414-39522020-07-016110.15826/umj.2020.1.012102DOMINATION AND EDGE DOMINATION IN TREESB. Senthilkumar0Yanamandram B. Venkatakrishnan1H. Naresh Kumar2SASTRA Deemed University, Tanjore, TamilnaduSASTRA Deemed University, Tanjore, TamilnaduSASTRA Deemed University, Tanjore, TamilnaduLet \(G=(V,E)\) be a simple graph. A set \(S\subseteq V\) is a dominating set if every vertex in \(V \setminus S\) is adjacent to a vertex in \(S\). The domination number of a graph \(G\), denoted by \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\). A set \(D \subseteq E\) is an edge dominating set if every edge in \(E\setminus D\) is adjacent to an edge in \(D\). The edge domination number of a graph \(G\), denoted by \(\gamma'(G)\) is the minimum cardinality of an edge dominating set of \(G\). We characterize trees with  domination number equal to twice edge domination number.https://umjuran.ru/index.php/umj/article/view/223edge dominating set, dominating set, trees.
spellingShingle B. Senthilkumar
Yanamandram B. Venkatakrishnan
H. Naresh Kumar
DOMINATION AND EDGE DOMINATION IN TREES
Ural Mathematical Journal
edge dominating set, dominating set, trees.
title DOMINATION AND EDGE DOMINATION IN TREES
title_full DOMINATION AND EDGE DOMINATION IN TREES
title_fullStr DOMINATION AND EDGE DOMINATION IN TREES
title_full_unstemmed DOMINATION AND EDGE DOMINATION IN TREES
title_short DOMINATION AND EDGE DOMINATION IN TREES
title_sort domination and edge domination in trees
topic edge dominating set, dominating set, trees.
url https://umjuran.ru/index.php/umj/article/view/223
work_keys_str_mv AT bsenthilkumar dominationandedgedominationintrees
AT yanamandrambvenkatakrishnan dominationandedgedominationintrees
AT hnareshkumar dominationandedgedominationintrees