  If ${\cal F}$ is a set of subgraphs $F$ of a finite graph $E$ we define a
graph-counting polynomial $$ p_{\cal F}(z)=\sum_{F\in{\cal F}}z^{|F|} $$ In the
present note we consider oriented graphs and discuss some cases where ${\cal
F}$ consists of unbranched subgraphs $E$. We find several situations where
something can be said about the location of the zeros of $p_{\cal F}$.
