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Characterization of trees with equal 2-domination number and domination number plus two

100%

Chellali M., Volkmann L.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 4

687-697

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.

Trees with equal 2-domination and 2-independence numbers

100%

Chellali M., Meddah N.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 2

263-270

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.

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2 Discussiones Mathematicae Graph Theory

2 Chellali M.

1 Meddah N.

1 Volkmann L.

1 2012

1 2011

Wyniki wyszukiwania

Characterization of trees with equal 2-domination number and domination number plus two

Trees with equal 2-domination and 2-independence numbers