On Dominating Sets and Independent Sets of Graphs

  title={On Dominating Sets and Independent Sets of Graphs},
  author={Jochen Harant and Anja Pruchnewski and Margit Voigt},
  journal={Combinatorics, Probability and Computing},
  pages={547 - 553}
For a graph G on vertex set V = {1, …, n} let k = (k1, …, kn) be an integral vector such that 1 [les ] ki [les ] di for i ∈ V, where di is the degree of the vertex i in G. A k-dominating set is a set Dk ⊆ V such that every vertex i ∈ V[setmn ]Dk has at least ki neighbours in Dk. The k-domination number γk(G) of G is the cardinality of a smallest k-dominating set of G. For k1 = · · · = kn = 1, k-domination corresponds to the usual concept of domination. Our approach yields an improvement of an… 
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Fundamente der Graphentheorie
  • L. Volkmann
  • Mathematics, Computer Science
    Springer Lehrbuch Mathematik
  • 1996
Dominating Sets and Independent Sets