Global Dominator Coloring of Graphs
Let S ⊆ V. A vertex v ∈ V is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let 𝒞 = (V1, V2, . . ., Vk) be a coloring of G and let v ∈ V (G). A color class Vi is called a dom-color class or an anti domcolor class...
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2019-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.2089 |
| _version_ | 1797757726594433024 |
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| author | Hamid Ismail Sahul Rajeswari Malairaj |
| author_facet | Hamid Ismail Sahul Rajeswari Malairaj |
| author_sort | Hamid Ismail Sahul |
| collection | DOAJ |
| description | Let S ⊆ V. A vertex v ∈ V is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let 𝒞 = (V1, V2, . . ., Vk) be a coloring of G and let v ∈ V (G). A color class Vi is called a dom-color class or an anti domcolor class of the vertex v according as v is a dominator of Vi or an antidominator of Vi. The coloring 𝒞 is called a global dominator coloring of G if every vertex of G has a dom-color class and an anti dom-color class in 𝒞. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number and is denoted by χgd(G). This paper initiates a study on this notion of global dominator coloring. |
| first_indexed | 2024-03-12T18:19:44Z |
| format | Article |
| id | doaj.art-f52345505f454115baef1fa2c042a604 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T18:19:44Z |
| publishDate | 2019-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-f52345505f454115baef1fa2c042a6042023-08-02T08:59:13ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922019-05-0139232533910.7151/dmgt.2089dmgt.2089Global Dominator Coloring of GraphsHamid Ismail Sahul0Rajeswari Malairaj1Department of Mathematics, The Madura College, Madurai – 11, IndiaDepartment of Mathematics, Fatima College, Madurai – 18, IndiaLet S ⊆ V. A vertex v ∈ V is a dominator of S if v dominates every vertex in S and v is said to be an anti-dominator of S if v dominates none of the vertices of S. Let 𝒞 = (V1, V2, . . ., Vk) be a coloring of G and let v ∈ V (G). A color class Vi is called a dom-color class or an anti domcolor class of the vertex v according as v is a dominator of Vi or an antidominator of Vi. The coloring 𝒞 is called a global dominator coloring of G if every vertex of G has a dom-color class and an anti dom-color class in 𝒞. The minimum number of colors required for a global dominator coloring of G is called the global dominator chromatic number and is denoted by χgd(G). This paper initiates a study on this notion of global dominator coloring.https://doi.org/10.7151/dmgt.2089global dominationcoloringglobal dominator coloringdominator coloring05c1505c69 |
| spellingShingle | Hamid Ismail Sahul Rajeswari Malairaj Global Dominator Coloring of Graphs Discussiones Mathematicae Graph Theory global domination coloring global dominator coloring dominator coloring 05c15 05c69 |
| title | Global Dominator Coloring of Graphs |
| title_full | Global Dominator Coloring of Graphs |
| title_fullStr | Global Dominator Coloring of Graphs |
| title_full_unstemmed | Global Dominator Coloring of Graphs |
| title_short | Global Dominator Coloring of Graphs |
| title_sort | global dominator coloring of graphs |
| topic | global domination coloring global dominator coloring dominator coloring 05c15 05c69 |
| url | https://doi.org/10.7151/dmgt.2089 |
| work_keys_str_mv | AT hamidismailsahul globaldominatorcoloringofgraphs AT rajeswarimalairaj globaldominatorcoloringofgraphs |