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Graph domination in distance two

Gábor BacsóAttila TálosZsolt Tuza — 2005

Discussiones Mathematicae Graph Theory

Let G = (V,E) be a graph, and k ≥ 1 an integer. A subgraph D is said to be k-dominating in G if every vertex of G-D is at distance at most k from some vertex of D. For a given class of graphs, Domₖ is the set of those graphs G in which every connected induced subgraph H has some k-dominating induced subgraph D ∈ which is also connected. In our notation, Dom coincides with Dom₁. In this paper we prove that D o m D o m u = D o m u holds for u = all connected graphs without induced P u (u ≥ 2). (In particular, ₂ = K₁ and...

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