Characterization of digraphs with equal domination graphs and underlying graphs

A domination graph of a digraph D, dom(D), is created using the vertex set of D and edge {u,v}@?E[dom(D)] whenever (u,z)@?A(D) or (v,z)@?A(D) for every other vertex [email protected]?V(D). The underlying graph of a digraph D, UG(D), is the graph for which D is a biorientation. We completely characterize digraphs whose underlying graphs are identical to their domination graphs, UG(D)=dom(D). The maximum and minimum number of single arcs in these digraphs, and their characteristics, is given.