Discussiones Mathematicae Graph Theory 32(2) (2012) 263-270
doi: 10.7151/dmgt.1603

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Trees with Equal 2-domination and 2-independence Numbers

Mustapha Chellali and Nacéra Meddah

LAMDA-RO Laboratory, Department of Mathematics
University of Blida
B.P. 270, Blida, Algeria


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.

Keywords: 2-domination number, 2-independence number, trees

2010 Mathematics Subject Classification: 05C69.


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Received 14 September 2010
Revised 10 May 2011
Accepted 11 May 2011