Geodesic
Reconfiguring Minimum Dominating Sets: The γ-Graph of a Tree
Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 3, pp. 703-716

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We consider γ-graphs, which are reconfiguration graphs of the minimum dominating sets of a graph G. We answer three open questions about γ-graphs of trees by providing upper bounds on the maximum degree, the diameter, and the number of minimum dominating sets. The latter gives an upper bound on the order of the γ-graph.
Keywords: domination, reconfiguration 
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Edwards, Michelle; MacGillivray, Gary; Nasserasr, Shahla. Reconfiguring Minimum Dominating Sets: The γ-Graph of a Tree. Discussiones Mathematicae. Graph Theory, Tome 38 (2018) no. 3, pp. 703-716. http://geodesic.mathdoc.fr/item/DMGT_2018_38_3_a6/