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Distance 2-Domination in Prisms of Graphs

100%

Hurtado F., Mora M., Rivera-Campo E., Zuazua R.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 2

383-397

A set of vertices D of a graph G is a distance 2-dominating set of G if the distance between each vertex u ∊ (V (G) − D) and D is at most two. Let γ2(G) denote the size of a smallest distance 2-dominating set of G. For any permutation π of the vertex set of G, the prism of G with respect to π is the graph πG obtained from G and a copy G′ of G by joining u ∊ V(G) with v′ ∊ V(G′) if and only if v′ = π(u). If γ2(πG) = γ2(G) for any permutation π of V(G), then G is called a universal γ2-fixer. In this work we characterize the cycles and paths that are universal γ2-fixers.

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Fractional domination in prisms

100%

Walsh M.

Discussiones Mathematicae Graph Theory

2007

tom 27

nr 3

541-547

Mynhardt has conjectured that if G is a graph such that γ(G) = γ(πG) for all generalized prisms πG then G is edgeless. The fractional analogue of this conjecture is established and proved by showing that, if G is a graph with edges, then $γ_f(G×K₂) > γ_f(G)$.

On the domination number of prisms of graphs

100%

Burger A., Mynhardt C., Weakley W.

Discussiones Mathematicae Graph Theory

2004

tom 24

nr 2

303-318

For a permutation π of the vertex set of a graph G, the graph π G is obtained from two disjoint copies G₁ and G₂ of G by joining each v in G₁ to π(v) in G₂. Hence if π = 1, then πG = K₂×G, the prism of G. Clearly, γ(G) ≤ γ(πG) ≤ 2 γ(G). We study graphs for which γ(K₂×G) = 2γ(G), those for which γ(πG) = 2γ(G) for at least one permutation π of V(G) and those for which γ(πG) = 2γ(G) for each permutation π of V(G).

Ograniczanie wyników

3 Discussiones Mathematicae Graph Theory

1 Burger A.

1 Hurtado F.

1 Mora M.

1 Mynhardt C.

1 Rivera-Campo E.

1 Walsh M.

1 Weakley W.

1 Zuazua R.

1 2017

1 2007

1 2004

Wyniki wyszukiwania

Distance 2-Domination in Prisms of Graphs

Fractional domination in prisms

On the domination number of prisms of graphs