graph product of groups

Let $\mathrm{\Gamma }$ be a finite undirected graph and let $\{G_v:v\in V(\mathrm{\Gamma })\}$ be a collection of groups associated with the vertices of $\mathrm{\Gamma }$. Then the graph product of the groups $G_v$ is the group $G=F/R$, where$F$ is the free product of the $G_v$ and $R$ is generated by the relations that elements of $G_u$ commute with elements of $G_v$ whenever $u$ and $v$ are adjacent in $\mathrm{\Gamma }$.

The free product and the direct product are the extreme examples of the graph product. To obtain the free product, let $\mathrm{\Gamma }$ be an anticlique, and to obtain the direct product, let $\mathrm{\Gamma }$ be a clique.