Independent strong domination in complementary prisms
<p class="p1">Let <em>G</em> = (<em>V, E</em>) be a graph and <em>u,v</em> ∈ <em>V</em>. Then, <em>u</em> strongly dominates<span class="Apple-converted-space"> </span><em>v</em><span cl...
| Main Authors: | , |
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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
2020-04-01
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| Series: | Electronic Journal of Graph Theory and Applications |
| Subjects: | |
| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/466 |
| _version_ | 1818531951539126272 |
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| author | Zeynep Nihan Berberler Murat Ersen Berberler |
| author_facet | Zeynep Nihan Berberler Murat Ersen Berberler |
| author_sort | Zeynep Nihan Berberler |
| collection | DOAJ |
| description | <p class="p1">Let <em>G</em> = (<em>V, E</em>) be a graph and <em>u,v</em> ∈ <em>V</em>. Then, <em>u</em> strongly dominates<span class="Apple-converted-space"> </span><em>v</em><span class="Apple-converted-space"> </span>if (i) <em>uv</em> ∈ <em>E</em><span class="Apple-converted-space"> </span>and (ii) deg(<em>u</em>) ≥ deg(<em>v</em>). A set <em>D</em> ⊂ <em>V</em> <span class="Apple-converted-space"> </span>is a strong-dominating set of<span class="Apple-converted-space"> </span><em>G</em><span class="Apple-converted-space"> </span>if every vertex in <em>V</em>-<em>D</em> is strongly dominated by at least one vertex in <em>D</em>. A set <em>D</em> ⊆ <em>V</em><span class="Apple-converted-space"> </span>is an independent set if no two vertices of <em>D</em><span class="Apple-converted-space"> </span>are adjacent. The independent strong domination number <em>i<sub>s</sub></em>(<em>G</em>)<span class="Apple-converted-space"> </span>of a graph <em>G</em><span class="Apple-converted-space"> </span>is the minimum cardinality of a strong dominating set which is independent. Let <em>Ġ</em> <span class="Apple-converted-space"> </span>be the complement of a graph <em>G</em>. The complementary prism <em>GĠ</em><span class="Apple-converted-space"> </span>of <em>G</em><span class="Apple-converted-space"> </span>is the graph formed from the disjoint union of <em>G</em><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><em>Ġ</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> <em>Ġ</em></span>. In this paper, we consider the independent strong domination in complementary prisms, characterize the complementary prisms with small independent strong domination numbers, and investigate the relationship between independent strong domination number and the distance-based parameters.</p> |
| first_indexed | 2024-12-11T17:39:10Z |
| format | Article |
| id | doaj.art-1f041d9d92ed421f88bfd3b7645144c0 |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-12-11T17:39:10Z |
| publishDate | 2020-04-01 |
| 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-1f041d9d92ed421f88bfd3b7645144c02022-12-22T00:56:35ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872020-04-01811810.5614/ejgta.2020.8.1.1162Independent strong domination in complementary prismsZeynep Nihan Berberler0Murat Ersen Berberler1Faculty of Science, Department of Computer Science, Dokuz Eylul University, 35160, Izmir/TurkeyFaculty of Science, Department of Computer Science, Dokuz Eylul University, 35160, Izmir/Turkey<p class="p1">Let <em>G</em> = (<em>V, E</em>) be a graph and <em>u,v</em> ∈ <em>V</em>. Then, <em>u</em> strongly dominates<span class="Apple-converted-space"> </span><em>v</em><span class="Apple-converted-space"> </span>if (i) <em>uv</em> ∈ <em>E</em><span class="Apple-converted-space"> </span>and (ii) deg(<em>u</em>) ≥ deg(<em>v</em>). A set <em>D</em> ⊂ <em>V</em> <span class="Apple-converted-space"> </span>is a strong-dominating set of<span class="Apple-converted-space"> </span><em>G</em><span class="Apple-converted-space"> </span>if every vertex in <em>V</em>-<em>D</em> is strongly dominated by at least one vertex in <em>D</em>. A set <em>D</em> ⊆ <em>V</em><span class="Apple-converted-space"> </span>is an independent set if no two vertices of <em>D</em><span class="Apple-converted-space"> </span>are adjacent. The independent strong domination number <em>i<sub>s</sub></em>(<em>G</em>)<span class="Apple-converted-space"> </span>of a graph <em>G</em><span class="Apple-converted-space"> </span>is the minimum cardinality of a strong dominating set which is independent. Let <em>Ġ</em> <span class="Apple-converted-space"> </span>be the complement of a graph <em>G</em>. The complementary prism <em>GĠ</em><span class="Apple-converted-space"> </span>of <em>G</em><span class="Apple-converted-space"> </span>is the graph formed from the disjoint union of <em>G</em><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> </span><em>Ġ</em> by adding the edges of a perfect matching between the corresponding vertices of <em>G</em><span class="Apple-converted-space"> </span>and<span class="Apple-converted-space"> <em>Ġ</em></span>. In this paper, we consider the independent strong domination in complementary prisms, characterize the complementary prisms with small independent strong domination numbers, and investigate the relationship between independent strong domination number and the distance-based parameters.</p>https://www.ejgta.org/index.php/ejgta/article/view/466domination, independent strong domination, complementary prisms, corona product |
| spellingShingle | Zeynep Nihan Berberler Murat Ersen Berberler Independent strong domination in complementary prisms Electronic Journal of Graph Theory and Applications domination, independent strong domination, complementary prisms, corona product |
| title | Independent strong domination in complementary prisms |
| title_full | Independent strong domination in complementary prisms |
| title_fullStr | Independent strong domination in complementary prisms |
| title_full_unstemmed | Independent strong domination in complementary prisms |
| title_short | Independent strong domination in complementary prisms |
| title_sort | independent strong domination in complementary prisms |
| topic | domination, independent strong domination, complementary prisms, corona product |
| url | https://www.ejgta.org/index.php/ejgta/article/view/466 |
| work_keys_str_mv | AT zeynepnihanberberler independentstrongdominationincomplementaryprisms AT muratersenberberler independentstrongdominationincomplementaryprisms |