A domination graph of a digraph
D,
dom(D), is created using the vertex set of
D and edge
d020712c685f3f536a4c50be9aa56a0f" title="Click to view the MathML source">{u,v}
E[dom(D)] whenever
13d811c431" title="Click to view the MathML source">(u,z)
A(D) or
(v,z)
A(D) for every other vertex
z
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.