Geodesic
γ-graphs of graphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 517-531

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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.
Keywords: dominating sets, gamma graphs 
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Fricke, Gerd; Hedetniemi, Sandra; Hedetniemi, Stephen; Hutson, Kevin. γ-graphs of graphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 3, pp. 517-531. http://geodesic.mathdoc.fr/item/DMGT_2011_31_3_a7/