  Aguiar and Ardila defined the Hopf monoid GP of generalized permutahedra and
showed that it contains many submonoids that correspond to combinatorial
objects. They also give a basic polynomial invariant of generalized
permutahedra, which then specializes to the submonoids. We define the Hopf
monoid of directed graphs and show that it also embeds in GP. The resulting
basic invariant coincides with the strict chromatic polynomial of Awan and
Bernardi.
