Let G = (V,E) be a graph. A subset S of V is a 2-dominating set if every vertex of V-S is dominated at least 2 times, and S is a 2-independent set of G if every vertex of S has at most one neighbor in S. The minimum cardinality of a 2-dominating set a of G is the 2-domination number γ₂(G) and the maximum cardinality of a 2-independent set of G is the 2-independence number β₂(G). Fink and Jacobson proved that γ₂(G) ≤ β₂(G) for every graph G. In this paper we provide a constructive characterization of trees with equal 2-domination and 2-independence numbers.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1603,
author = {Mustapha Chellali and Nac\'era Meddah},
title = {Trees with equal 2-domination and 2-independence numbers},
journal = {Discussiones Mathematicae Graph Theory},
volume = {32},
year = {2012},
pages = {263-270},
zbl = {1255.05131},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1603}
}
Mustapha Chellali; Nacéra Meddah. Trees with equal 2-domination and 2-independence numbers. Discussiones Mathematicae Graph Theory, Tome 32 (2012) pp. 263-270. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1603/
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