- Tytuł:
- The k-Rainbow Bondage Number of a Digraph
- Autorzy:
-
Amjadi, Jafar
Mohammadi, Negar
Sheikholeslami, Seyed Mahmoud
Volkmann, Lutz - Powiązania:
- https://bibliotekanauki.pl/articles/31339490.pdf
- Data publikacji:
- 2015-05-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
k-rainbow dominating function
k-rainbow domination number
k-rainbow bondage number
digraph - Opis:
- Let $ D = (V,A) $ be a finite and simple digraph. A $k$-rainbow dominating function ($ k \text{RDF} $) 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 \in V $ with $ f(v) = \emptyset $ the condition \( \bigcup_{ u \in N^−(v) } f(u) = {1, 2, . . ., k} \) is fulfilled, where $ N^− (v) $ is the set of in-neighbors of $v$. The weight of a \( k \text{RDF} \) \( f \) is the value \( \omega (f) = \sum_{v \in V} |f(v)| \). The $k$-rainbow domination number of a digraph $D$, denoted by $ \gamma_{rk} (D) $, is the minimum weight of a $ k \text{RDF} $ of $D$. The $k$-rainbow bondage number $ b_{rk} (D) $ of a digraph $D$ with maximum in-degree at least two, is the minimum cardinality of all sets $ A^\prime \subseteq A $ for which $ \gamma_{rk} (D−A^\prime ) > \gamma_{rk} (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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2015, 35, 2; 261-270
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł