Connected domination value in graphs
<p class="p1">In a connected graph <em>G</em> = (<em>V,E</em>), a set <em>D</em> ⊂ <em>V</em> is a <em>connected dominating set</em> if for every vertex <em>v</em> ∈ <em>V </em>\ <em>D</em>...
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| Format: | Article |
| Language: | English |
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Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia
2021-04-01
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| Series: | Electronic Journal of Graph Theory and Applications |
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| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/736 |
| _version_ | 1818531923774930944 |
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| author | Angsuman Das |
| author_facet | Angsuman Das |
| author_sort | Angsuman Das |
| collection | DOAJ |
| description | <p class="p1">In a connected graph <em>G</em> = (<em>V,E</em>), a set <em>D</em> ⊂ <em>V</em> is a <em>connected dominating set</em> if for every vertex <em>v</em> ∈ <em>V </em>\ <em>D</em>, there exists <em>u</em> ∈ <em>D</em> such that <em>u</em> and <em>v</em> are adjacent, and the subgraph〈<em>D</em>〉induced by <em>D</em> in <em>G</em> is connected. A connected dominating set of minimum cardinality is called a <em>γ<sub>c</sub></em>-set of <em>G</em>. For each vertex <em>v</em> ∈ <em>V</em>, we define the <em>connected domination value</em> of <em>v</em> to be the number of <em>γ<sub>c</sub></em>-sets of <em>G</em> to which <em>v</em> belongs. In this paper, we study the properties of connected domination value of a connected graph <em>G</em> and its relation to other parameters of a connected graph. Finally, we compute the connected domination value and number of <em>γ<sub>c</sub></em>-sets for a few well-known family of graphs.</p> |
| first_indexed | 2024-12-11T17:38:48Z |
| format | Article |
| id | doaj.art-cf9b363f4ce54855a39129b9f2216520 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-12-11T17:38:48Z |
| publishDate | 2021-04-01 |
| publisher | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia |
| record_format | Article |
| series | Electronic Journal of Graph Theory and Applications |
| spelling | doaj.art-cf9b363f4ce54855a39129b9f22165202022-12-22T00:56:36ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872021-04-019111312310.5614/ejgta.2021.9.1.11207Connected domination value in graphsAngsuman Das0Department of Mathematics, Presidency University, Kolkata, India.<p class="p1">In a connected graph <em>G</em> = (<em>V,E</em>), a set <em>D</em> ⊂ <em>V</em> is a <em>connected dominating set</em> if for every vertex <em>v</em> ∈ <em>V </em>\ <em>D</em>, there exists <em>u</em> ∈ <em>D</em> such that <em>u</em> and <em>v</em> are adjacent, and the subgraph〈<em>D</em>〉induced by <em>D</em> in <em>G</em> is connected. A connected dominating set of minimum cardinality is called a <em>γ<sub>c</sub></em>-set of <em>G</em>. For each vertex <em>v</em> ∈ <em>V</em>, we define the <em>connected domination value</em> of <em>v</em> to be the number of <em>γ<sub>c</sub></em>-sets of <em>G</em> to which <em>v</em> belongs. In this paper, we study the properties of connected domination value of a connected graph <em>G</em> and its relation to other parameters of a connected graph. Finally, we compute the connected domination value and number of <em>γ<sub>c</sub></em>-sets for a few well-known family of graphs.</p>https://www.ejgta.org/index.php/ejgta/article/view/736domination value, connected dominating set, maximum degree |
| spellingShingle | Angsuman Das Connected domination value in graphs Electronic Journal of Graph Theory and Applications domination value, connected dominating set, maximum degree |
| title | Connected domination value in graphs |
| title_full | Connected domination value in graphs |
| title_fullStr | Connected domination value in graphs |
| title_full_unstemmed | Connected domination value in graphs |
| title_short | Connected domination value in graphs |
| title_sort | connected domination value in graphs |
| topic | domination value, connected dominating set, maximum degree |
| url | https://www.ejgta.org/index.php/ejgta/article/view/736 |
| work_keys_str_mv | AT angsumandas connecteddominationvalueingraphs |