  We prove three results about the graph product $G=\G(\Gamma;G_v, v \in
V(\Gamma))$ of groups $G_v$ over a graph $\Gamma$. The first result generalises
a result of Servatius, Droms and Servatius, proved by them for right-angled
Artin groups; we prove a necessary and sufficient condition on a finite graph
$\Gamma$ for the kernel of the map from $G$ to the associated direct product to
be free (one part of this result already follows from a result in S. Kim's
Ph.D. thesis). The second result generalises a result of Hermiller and Sunic,
again from right-angled Artin groups; we prove that for a graph $\Gamma$ with
finite chromatic number, $G$ has a series in which every factor is a free
product of vertex groups. The third result provides an alternative proof of a
theorem due to Meier, which provides necessary and sufficient conditions on a
finite graph $\Gamma$ for $G$ to be hyperbolic.
