Graph-Counting Polynomials for Oriented Graphs

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