# On Dominating Sets and Independent Sets of Graphs

@article{Harant1999OnDS,
title={On Dominating Sets and Independent Sets of Graphs},
author={Jochen Harant and Anja Pruchnewski and Margit Voigt},
journal={Combinatorics, Probability and Computing},
year={1999},
volume={8},
pages={547 - 553}
}
• Published 1 November 1999
• Mathematics
• Combinatorics, Probability and Computing
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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Dominating Sets and Independent Sets