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- Dirk Meierling, Seyed Mahmoud Sheikholeslami, Lutz Volkmann
- Appl. Math. Lett.
- 2011

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… (More)

- Dirk Meierling, Lutz Volkmann
- Math. Meth. of OR
- 2009

- Dirk Meierling, Lutz Volkmann, Stephan Zitzen
- Discrete Applied Mathematics
- 2009

- Adriana Hansberg, Dirk Meierling, Lutz Volkmann
- Electr. J. Comb.
- 2007

A set D ⊆ V of vertices is said to be a (connected) distance k-dominating set of G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected) distance k-dominating set in G is the (connected) distance k-domination number of G, denoted by γ k (G) (γ c k (G), respectively).… (More)

- Adriana Hansberg, Dirk Meierling, Lutz Volkmann
- Int. J. Comput. Math.
- 2011

- Dirk Meierling, Lutz Volkmann
- Discrete Mathematics
- 2008

- Torsten Korneffel, Dirk Meierling, Lutz Volkmann
- Discussiones Mathematicae Graph Theory
- 2008

A subset D of the vertex set of a graph G is a (k, p)-dominating set if every vertex v ∈ V (G) \ D is within distance k to at least p vertices in D. The parameter γ k,p (G) denotes the minimum cardinality of a (k, p)-dominating set of G. In 1994, Bean, Henning and Swart posed the conjecture that γ k,p (G) ≤ p p+k n(G) for any graph G with δ k (G) ≥ k + p −… (More)

- Andreas Holtkamp, Dirk Meierling, Luis Pedro Montejano
- Discrete Applied Mathematics
- 2012

- Zhihong He, Torsten Korneffel, Dirk Meierling, Lutz Volkmann, Stefan Winzen
- Discrete Mathematics
- 2009

- Dirk Meierling, Lutz Volkmann
- Discrete Applied Mathematics
- 2012