- Tytuł:
- The k-rainbow domatic number of a graph
- Autorzy:
-
Sheikholeslami, Seyyed
Volkmann, Lutz - Powiązania:
- https://bibliotekanauki.pl/articles/743715.pdf
- Data publikacji:
- 2012
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
k-rainbow dominating function
k-rainbow domination number
k-rainbow domatic number - Opis:
- For a positive integer k, a k-rainbow dominating function of a graph G is a function f from the vertex set V(G) to the set of all subsets of the set {1,2, ...,k} such that for any vertex v ∈ V(G) with f(v) = ∅ the condition ⋃_{u ∈ N(v)}f(u) = {1,2, ...,k} is fulfilled, where N(v) is the neighborhood of v. The 1-rainbow domination is the same as the ordinary domination. A set ${f₁,f₂, ...,f_d}$ of k-rainbow dominating functions on G with the property that $∑_{i = 1}^d |f_i(v)| ≤ k$ for each v ∈ V(G), is called a k-rainbow dominating family (of functions) on G. The maximum number of functions in a k-rainbow dominating family on G is the k-rainbow domatic number of G, denoted by $d_{rk}(G)$. Note that $d_{r1}(G)$ is the classical domatic number d(G). In this paper we initiate the study of the k-rainbow domatic number in graphs and we present some bounds for $d_{rk}(G)$. Many of the known bounds of d(G) are immediate consequences of our results.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2012, 32, 1; 129-140
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł