The k-Rainbow Bondage Number of a Digraph
Let D = (V,A) be a finite and simple digraph. A k-rainbow dominating function (kRDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V with f(v) = Ø the condition ∪u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled,...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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University of Zielona Góra
2015-05-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | https://doi.org/10.7151/dmgt.1797 |
| _version_ | 1797704410080477184 |
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| author | Amjadi Jafar Mohammadi Negar Sheikholeslami Seyed Mahmoud Volkmann Lutz |
| author_facet | Amjadi Jafar Mohammadi Negar Sheikholeslami Seyed Mahmoud Volkmann Lutz |
| author_sort | Amjadi Jafar |
| collection | DOAJ |
| description | Let D = (V,A) be a finite and simple digraph. A k-rainbow dominating function (kRDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V with f(v) = Ø the condition ∪u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. The weight of a kRDF f is the value w(f) = ∑v∈V |f(v)|. The k-rainbow domination number of a digraph D, denoted by γrk(D), is the minimum weight of a kRDF of D. The k-rainbow bondage number brk(D) of a digraph D with maximum in-degree at least two, is the minimum cardinality of all sets A′ ⊆ A for which γrk(D−A′) > γrk(D). In this paper, we establish some bounds for the k-rainbow bondage number and determine the k-rainbow bondage number of several classes of digraphs. |
| first_indexed | 2024-03-12T05:19:58Z |
| format | Article |
| id | doaj.art-a521981befcb49aa96d668fec295c091 |
| institution | Directory Open Access Journal |
| issn | 2083-5892 |
| language | English |
| last_indexed | 2024-03-12T05:19:58Z |
| publishDate | 2015-05-01 |
| publisher | University of Zielona Góra |
| record_format | Article |
| series | Discussiones Mathematicae Graph Theory |
| spelling | doaj.art-a521981befcb49aa96d668fec295c0912023-09-03T07:47:23ZengUniversity of Zielona GóraDiscussiones Mathematicae Graph Theory2083-58922015-05-0135226127010.7151/dmgt.1797dmgt.1797The k-Rainbow Bondage Number of a DigraphAmjadi Jafar0Mohammadi Negar1Sheikholeslami Seyed Mahmoud2Volkmann Lutz3Department of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. IranDepartment of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. IranDepartment of Mathematics Azarbaijan Shahid Madani University Tabriz, I.R. IranLehrstuhl II für Mathematik RWTH Aachen University 52056 Aachen, GermanyLet D = (V,A) be a finite and simple digraph. A k-rainbow dominating function (kRDF) of a digraph D is a function f from the vertex set V to the set of all subsets of the set {1, 2, . . . , k} such that for any vertex v ∈ V with f(v) = Ø the condition ∪u∈N−(v) f(u) = {1, 2, . . . , k} is fulfilled, where N−(v) is the set of in-neighbors of v. The weight of a kRDF f is the value w(f) = ∑v∈V |f(v)|. The k-rainbow domination number of a digraph D, denoted by γrk(D), is the minimum weight of a kRDF of D. The k-rainbow bondage number brk(D) of a digraph D with maximum in-degree at least two, is the minimum cardinality of all sets A′ ⊆ A for which γrk(D−A′) > γrk(D). In this paper, we establish some bounds for the k-rainbow bondage number and determine the k-rainbow bondage number of several classes of digraphs.https://doi.org/10.7151/dmgt.1797k-rainbow dominating functionk-rainbow domination numberk-rainbow bondage numberdigraph |
| spellingShingle | Amjadi Jafar Mohammadi Negar Sheikholeslami Seyed Mahmoud Volkmann Lutz The k-Rainbow Bondage Number of a Digraph Discussiones Mathematicae Graph Theory k-rainbow dominating function k-rainbow domination number k-rainbow bondage number digraph |
| title | The k-Rainbow Bondage Number of a Digraph |
| title_full | The k-Rainbow Bondage Number of a Digraph |
| title_fullStr | The k-Rainbow Bondage Number of a Digraph |
| title_full_unstemmed | The k-Rainbow Bondage Number of a Digraph |
| title_short | The k-Rainbow Bondage Number of a Digraph |
| title_sort | k rainbow bondage number of a digraph |
| topic | k-rainbow dominating function k-rainbow domination number k-rainbow bondage number digraph |
| url | https://doi.org/10.7151/dmgt.1797 |
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