Let G = (V(G),E(G)) be a simple graph, and let k be a positive integer. A subset D of V(G) is a k-dominating set if every vertex of V(G) - D is dominated at least k times by D. The k-domination number γₖ(G) is the minimum cardinality of a k-dominating set of G. In [5] Volkmann showed that for every nontrivial tree T, γ₂(T) ≥ γ₁(T)+1 and characterized extremal trees attaining this bound. In this paper we characterize all trees T with γ₂(T) = γ₁(T)+2.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1573,
author = {Mustapha Chellali and Lutz Volkmann},
title = {Characterization of trees with equal 2-domination number and domination number plus two},
journal = {Discussiones Mathematicae Graph Theory},
volume = {31},
year = {2011},
pages = {687-697},
zbl = {1255.05132},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1573}
}
Mustapha Chellali; Lutz Volkmann. Characterization of trees with equal 2-domination number and domination number plus two. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 687-697. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1573/
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