Digraphs with isomorphic underlying and domination graphs: Connected UGc(D)
Discussiones Mathematicae Graph Theory
The domination graph of a directed graph has an edge between vertices x and y provided either (x,z) or (y,z) is an arc for every vertex z distinct from x and y. We consider directed graphs D for which the domination graph of D is isomorphic to the underlying graph of D. We demonstrate that the complement of the underlying graph must have k connected components isomorphic to complete graphs, paths, or cycles. A complete characterization of directed graphs where k = 1 is presented.
Factor, K. A.,
Langley, L. L.
Digraphs with isomorphic underlying and domination graphs: Connected UGc(D).
Discussiones Mathematicae Graph Theory, 27(1), 51–68.