  Let D be a simple digraph without loops or digons. For any v in V(D) let
N_1(v) be the set of all nodes at out-distance 1 from v and let N_2(v) be the
set of all nodes at out-distance 2. We provide sufficient conditions under
which there must exist some v in V(D) such that |N_1(v)| is less than or equal
to |N_2(v)|, as well as examine properties of a minimal graph which does not
have such a node. We show that if one such graph exists, then there exist
infinitely many strongly-connected graphs having no such vertex.
