Independent Restrained k - Rainbow Dominating Function
Let G be a graph and let f be a function that assigns to each vertex a set of colors chosen from the set {1, 2…, k} that is f: V(G) P [1,2,…,k]. If for each vertex v V(G) such that f(v) = .we have then f is called the k – Rainbow Dominating Function (KRDF) of G. A k – Rainbow Dominating Function...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Accademia Piceno Aprutina dei Velati
2022-12-01
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| Series: | Ratio Mathematica |
| Subjects: | |
| Online Access: | http://eiris.it/ojs/index.php/ratiomathematica/article/view/924 |
| _version_ | 1811204189189046272 |
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| author | M Esakki Dharani A Nagarajan K Palani |
| author_facet | M Esakki Dharani A Nagarajan K Palani |
| author_sort | M Esakki Dharani |
| collection | DOAJ |
| description | Let G be a graph and let f be a function that assigns to each vertex a set of colors chosen from the set {1, 2…, k} that is f: V(G) P [1,2,…,k]. If for each vertex v V(G) such that f(v) = .we have then f is called the k – Rainbow Dominating Function (KRDF) of G. A k – Rainbow Dominating Function is said to be Independent Restrained k - Rainbow Dominating function if (i)The set of vertices assigned with non – empty set is independent. (ii)The induced subgraph of G, by the vertices with label has no isolated vertices. The weight w(f) of a function f is defined as w(f) = .The Independent Restrained k – Rainbow Domination number is the minimum weight of G. In this paper we introduce Independent Restrained k – Rainbow Domination and find for some graphs |
| first_indexed | 2024-04-12T03:08:12Z |
| format | Article |
| id | doaj.art-4672dda8baea454c9d5ece694c0cfcb2 |
| institution | Directory Open Access Journal |
| issn | 1592-7415 2282-8214 |
| language | English |
| last_indexed | 2024-04-12T03:08:12Z |
| publishDate | 2022-12-01 |
| publisher | Accademia Piceno Aprutina dei Velati |
| record_format | Article |
| series | Ratio Mathematica |
| spelling | doaj.art-4672dda8baea454c9d5ece694c0cfcb22022-12-22T03:50:27ZengAccademia Piceno Aprutina dei VelatiRatio Mathematica1592-74152282-82142022-12-0144034935310.23755/rm.v44i0.924640Independent Restrained k - Rainbow Dominating FunctionM Esakki Dharani0A Nagarajan1K Palani2Research Scholar (Reg.No.21212232092011), PG& Research Department of Mathematics, V.O. Chidambaram College, Thoothukudi-628008, Tamil Nadu, India.Affiliated to ManonmaniamSundaranar University,Abishekapatti, Tirunelveli-627012, Tamil Nadu, IndiaAssociate Professor (Retd.), V.O. Chidambaram College, Thoothukudi-628008, Tamil Nadu, India Affiliated to Manonmaniam Sundaranar University,Abishekapatti, Tirunelveli-627012,AssociateProfessor, A.P.C.Mahalaxmi College for Women, Thoothukudi-628008, Tamil Nadu, India.Affiliated to Manonmaniam Sundaranar University,Abishekapatti, Tirunelveli-627012Let G be a graph and let f be a function that assigns to each vertex a set of colors chosen from the set {1, 2…, k} that is f: V(G) P [1,2,…,k]. If for each vertex v V(G) such that f(v) = .we have then f is called the k – Rainbow Dominating Function (KRDF) of G. A k – Rainbow Dominating Function is said to be Independent Restrained k - Rainbow Dominating function if (i)The set of vertices assigned with non – empty set is independent. (ii)The induced subgraph of G, by the vertices with label has no isolated vertices. The weight w(f) of a function f is defined as w(f) = .The Independent Restrained k – Rainbow Domination number is the minimum weight of G. In this paper we introduce Independent Restrained k – Rainbow Domination and find for some graphshttp://eiris.it/ojs/index.php/ratiomathematica/article/view/924independent, restrained, rainbow domination number, weight |
| spellingShingle | M Esakki Dharani A Nagarajan K Palani Independent Restrained k - Rainbow Dominating Function Ratio Mathematica independent, restrained, rainbow domination number, weight |
| title | Independent Restrained k - Rainbow Dominating Function |
| title_full | Independent Restrained k - Rainbow Dominating Function |
| title_fullStr | Independent Restrained k - Rainbow Dominating Function |
| title_full_unstemmed | Independent Restrained k - Rainbow Dominating Function |
| title_short | Independent Restrained k - Rainbow Dominating Function |
| title_sort | independent restrained k rainbow dominating function |
| topic | independent, restrained, rainbow domination number, weight |
| url | http://eiris.it/ojs/index.php/ratiomathematica/article/view/924 |
| work_keys_str_mv | AT mesakkidharani independentrestrainedkrainbowdominatingfunction AT anagarajan independentrestrainedkrainbowdominatingfunction AT kpalani independentrestrainedkrainbowdominatingfunction |