γ-graphs of graphs
Gerd H. Fricke, Sandra M. Hedetniemi, Stephen T. Hedetniemi, Kevin R. Hutson · Discussiones Mathematicae Graph Theory · 2011
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 γgraph 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 D 1 and D 2 , are adjacent in E(γ) if there exists a vertex v ∈ D 1 and a vertex w ∈ D 2 such that v is adjacent to w and D 1 = D 2 -{w} ∪ {v}, or equivalently, D 2 = D 1 -{v} ∪ {w}.In this paper we initiate the study of γ-graphs of graphs.