Characterization of digraphs with equal domination graphs and underlying graphs Original Research Article

A domination graph of a digraph D, image, is created using the vertex set of D and edge image whenever image or image for every other vertex image. The underlying graph of a digraph image, image, is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, image. The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given.