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γ-graphs of graphs

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Fricke G., Hedetniemi S., Hedetniemi S., Hutson K.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 3

517-531

A set S ⊆ V is a dominating set of a graph G = (V,E) if every vertex in V -S is adjacent to at least one vertex in S. The domination number γ(G) of G equals the minimum cardinality of a dominating set S in G; we say that such a set S is a γ-set. In this paper we consider the family of all γ-sets in a graph G and we define the γ-graph G(γ) = (V(γ), E(γ)) of G to be the graph whose vertices V(γ) correspond 1-to-1 with the γ-sets of G, and two γ-sets, say D₁ and D₂, are adjacent in E(γ) if there exists a vertex v ∈ D₁ and a vertex w ∈ D₂ such that v is adjacent to w and D₁ = D₂ - {w} ∪ {v}, or equivalently, D₂ = D₁ - {v} ∪ {w}. In this paper we initiate the study of γ-graphs of graphs.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Fricke G.

1 Hedetniemi S.

1 Hutson K.

1 2011

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γ-graphs of graphs