  In this paper we initialize the study of independent domination in directed
graphs. We show that an independent dominating set of an orientation of a graph
is also an independent dominating set of the underlying graph, but that the
converse is not true in general. We then prove existence and uniqueness
theorems for several classes of digraphs including orientations of complete
graphs, paths, trees, DAGs, cycles, and bipartite graphs. We also provide the
idomatic number for special cases of some of these families of digraphs.
