Surface subgroups of graph groups

Given a graph $ \Gamma $ $ {F_\Gamma }$, with a defining relation $ xy = yx$ of adjacent vertices of $ \Gamma $ $ {F_\Gamma }$ is an $ n$ $ (n \geq 4)$ $ {F'_\Gamma }$ $ 1 + (n - 4){2^{n - 3}}$ for which <IMG WIDTH="30" HEIGHT="41" ALIGN="MIDDLE" BORDER="0" SRC="images/img14.gif" ALT="$ {F'_\Gamma }$"> is a free group.