Isoperimetric functions for graph products

AbstractLet Γ be a finite graph, and for each vertex i let Gi be a finitely presented group. Let G be the graph product of the Gi. That is, G is the group obtained from the free product of the Gi by factoring out by the smallest normal subgroup containing all [g, h] where g EGi and h Gj and there is an edge joining i and j. We show that G has an isoperimetric function of degree k > 1 (or an exponential isoperimetric function) if each vertex group has such an isoperimetric function