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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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
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| 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. |
| format | Article |
| id | doaj-art-ee03f48e4bc445eaba1a2864dca43cbf |
| 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 |