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

Generalising some results about right-angled Artin groups to graph products of groups