Roman domination in oriented trees
<p class="p1">Let <em>D</em>=(<em>V,A</em>) be a digraph of order <em>n</em> = |<em>V</em>|. A <em>Roman dominating function</em> of a digraph <em>D</em> is a function <em>f</em> : <em>V </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 |
| Subjects: | |
| Online Access: | https://www.ejgta.org/index.php/ejgta/article/view/571 |
| _version_ | 1811335744094994432 |
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| author | Lyes Ouldrabah Mostafa Blidia Ahmed Bouchou |
| author_facet | Lyes Ouldrabah Mostafa Blidia Ahmed Bouchou |
| author_sort | Lyes Ouldrabah |
| collection | DOAJ |
| description | <p class="p1">Let <em>D</em>=(<em>V,A</em>) be a digraph of order <em>n</em> = |<em>V</em>|. A <em>Roman dominating function</em> of a digraph <em>D</em> is a function <em>f</em> : <em>V </em> → {0,1,2} such that every vertex <em>u</em> for which <em>f</em>(<em>u</em>) = 0 has an in-neighbor <em>v</em> for which <em>f</em>(<em>v</em>) = 2. The weight of a <em>Roman dominating function</em> is the value <em>f</em>(<em>V</em>)=∑<sub>u∈V </sub><em>f</em>(<em>u</em>). The minimum weight of a <em>Roman dominating function</em> of a digraph <em>D</em> is called the <em>Roman domination number</em> of <em>D</em>, denoted by <em>γ<sub>R</sub></em>(<em>D</em>). In this paper, we characterize oriented trees <em>T</em> satisfying <em>γ<sub>R</sub></em>(<em>T</em>)+Δ<sup>+</sup>(<em>T</em>) = <em>n</em>+1.</p><p class="p2"> </p> |
| first_indexed | 2024-04-13T17:29:38Z |
| format | Article |
| id | doaj.art-7ef95957ff334d99acf17f66b919dc2a |
| institution | Directory Open Access Journal |
| issn | 2338-2287 |
| language | English |
| last_indexed | 2024-04-13T17:29:38Z |
| 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-7ef95957ff334d99acf17f66b919dc2a2022-12-22T02:37:37ZengIndonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), IndonesiaElectronic Journal of Graph Theory and Applications2338-22872021-04-01919510310.5614/ejgta.2021.9.1.9205Roman domination in oriented treesLyes Ouldrabah0Mostafa Blidia1Ahmed Bouchou2Department of Mathematics, University of Blida 1. B.P. 270, Blida, AlgeriaDepartment of Mathematics, University of Blida 1. B.P. 270, Blida, AlgeriaDepartment of Mathematics, University of Medea, Algeria<p class="p1">Let <em>D</em>=(<em>V,A</em>) be a digraph of order <em>n</em> = |<em>V</em>|. A <em>Roman dominating function</em> of a digraph <em>D</em> is a function <em>f</em> : <em>V </em> → {0,1,2} such that every vertex <em>u</em> for which <em>f</em>(<em>u</em>) = 0 has an in-neighbor <em>v</em> for which <em>f</em>(<em>v</em>) = 2. The weight of a <em>Roman dominating function</em> is the value <em>f</em>(<em>V</em>)=∑<sub>u∈V </sub><em>f</em>(<em>u</em>). The minimum weight of a <em>Roman dominating function</em> of a digraph <em>D</em> is called the <em>Roman domination number</em> of <em>D</em>, denoted by <em>γ<sub>R</sub></em>(<em>D</em>). In this paper, we characterize oriented trees <em>T</em> satisfying <em>γ<sub>R</sub></em>(<em>T</em>)+Δ<sup>+</sup>(<em>T</em>) = <em>n</em>+1.</p><p class="p2"> </p>https://www.ejgta.org/index.php/ejgta/article/view/571roman domination, digraph, oriented tree |
| spellingShingle | Lyes Ouldrabah Mostafa Blidia Ahmed Bouchou Roman domination in oriented trees Electronic Journal of Graph Theory and Applications roman domination, digraph, oriented tree |
| title | Roman domination in oriented trees |
| title_full | Roman domination in oriented trees |
| title_fullStr | Roman domination in oriented trees |
| title_full_unstemmed | Roman domination in oriented trees |
| title_short | Roman domination in oriented trees |
| title_sort | roman domination in oriented trees |
| topic | roman domination, digraph, oriented tree |
| url | https://www.ejgta.org/index.php/ejgta/article/view/571 |
| work_keys_str_mv | AT lyesouldrabah romandominationinorientedtrees AT mostafablidia romandominationinorientedtrees AT ahmedbouchou romandominationinorientedtrees |