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Characterization of block graphs with equal 2-domination number and domination number plus one

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Hansberg A., Volkmann L.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 1

93-103

Let G be a simple graph, and let p be a positive integer. A subset D ⊆ V(G) is a p-dominating set of the graph G, if every vertex v ∈ V(G)-D is adjacent with at least p vertices of D. The p-domination number γₚ(G) is the minimum cardinality among the p-dominating sets of G. Note that the 1-domination number γ₁(G) is the usual domination number γ(G). If G is a nontrivial connected block graph, then we show that γ₂(G) ≥ γ(G)+1, and we characterize all connected block graphs with γ₂(G) = γ(G)+1. Our results generalize those of Volkmann [12] for trees.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Hansberg A.

1 Volkmann L.

1 2007

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Characterization of block graphs with equal 2-domination number and domination number plus one