Graph-counting polynomials for oriented graphs

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