Twin signed domination numbers in directed graphs
Let \(D=(V,A)\) be a finite simple directed graph (shortly digraph). A function \(f:V\longrightarrow \{-1,1\}\) is called a twin signed dominating function (TSDF) if \(f(N^-[v])\ge 1\) and \(f(N^+[v])\ge 1\) for each vertex \(v\in V\). The twin signed domination number of \(D\) is \(\gamma_{s}^*(D)=...
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| Datum: | 2017 |
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| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2017
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/21 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543251550437376 |
|---|---|
| author | Atapour, Maryam Norouzian, Sepideh Sheikholeslami, Seyed Mahmoud Volkmann, Lutz |
| author_facet | Atapour, Maryam Norouzian, Sepideh Sheikholeslami, Seyed Mahmoud Volkmann, Lutz |
| author_sort | Atapour, Maryam |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-10-11T02:04:21Z |
| description | Let \(D=(V,A)\) be a finite simple directed graph (shortly digraph). A function \(f:V\longrightarrow \{-1,1\}\) is called a twin signed dominating function (TSDF) if \(f(N^-[v])\ge 1\) and \(f(N^+[v])\ge 1\) for each vertex \(v\in V\). The twin signed domination number of \(D\) is \(\gamma_{s}^*(D)=\min\{\omega(f)\mid f \text{ is a TSDF of } D\}\). In this paper, we initiate the study of twin signed domination in digraphs and we present sharp lower bounds for \(\gamma_{s}^*(D)\) in terms of the order, size and maximum and minimum indegrees and outdegrees. Some of our results are extensions of well-known lower bounds of the classical signed domination numbers of graphs. |
| first_indexed | 2025-12-02T15:30:53Z |
| format | Article |
| id | admjournalluguniveduua-article-21 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:30:53Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-212017-10-11T02:04:21Z Twin signed domination numbers in directed graphs Atapour, Maryam Norouzian, Sepideh Sheikholeslami, Seyed Mahmoud Volkmann, Lutz twin signed dominating function, twin signed domination number 05C69 Let \(D=(V,A)\) be a finite simple directed graph (shortly digraph). A function \(f:V\longrightarrow \{-1,1\}\) is called a twin signed dominating function (TSDF) if \(f(N^-[v])\ge 1\) and \(f(N^+[v])\ge 1\) for each vertex \(v\in V\). The twin signed domination number of \(D\) is \(\gamma_{s}^*(D)=\min\{\omega(f)\mid f \text{ is a TSDF of } D\}\). In this paper, we initiate the study of twin signed domination in digraphs and we present sharp lower bounds for \(\gamma_{s}^*(D)\) in terms of the order, size and maximum and minimum indegrees and outdegrees. Some of our results are extensions of well-known lower bounds of the classical signed domination numbers of graphs. Lugansk National Taras Shevchenko University 2017-10-07 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/21 Algebra and Discrete Mathematics; Vol 24, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/21/pdf Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | twin signed dominating function twin signed domination number 05C69 Atapour, Maryam Norouzian, Sepideh Sheikholeslami, Seyed Mahmoud Volkmann, Lutz Twin signed domination numbers in directed graphs |
| title | Twin signed domination numbers in directed graphs |
| title_full | Twin signed domination numbers in directed graphs |
| title_fullStr | Twin signed domination numbers in directed graphs |
| title_full_unstemmed | Twin signed domination numbers in directed graphs |
| title_short | Twin signed domination numbers in directed graphs |
| title_sort | twin signed domination numbers in directed graphs |
| topic | twin signed dominating function twin signed domination number 05C69 |
| topic_facet | twin signed dominating function twin signed domination number 05C69 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/21 |
| work_keys_str_mv | AT atapourmaryam twinsigneddominationnumbersindirectedgraphs AT norouziansepideh twinsigneddominationnumbersindirectedgraphs AT sheikholeslamiseyedmahmoud twinsigneddominationnumbersindirectedgraphs AT volkmannlutz twinsigneddominationnumbersindirectedgraphs |