Semistability of graph products

A {\it graph product} $G$ on a $\Gamma$ is group defined as follows: For each vertex $v$ of there corresponding non-trivial $G_v$. The the quotient free product $G_v$ by commutation relations $[G_v,G_w]=1$ for all adjacent and $w$ in $\Gamma$. finitely presented has semistable fundamental at $\infty$} if some (equivalently any) finite connected CW-complex $X$ with $\pi_1(X)=G$, universal cover $\tilde X$ property that any two proper rays are properly homotopic. class groups $\infty$ known to contain many other classes groups, but it 40 year old question whether or not have $\infty$. Our main theorem combination result. It states presented, then non-semistable only such semistable, subgroup generated vertices $lk(v)$ complete finite). Hence one knows which finite, an elementary inspection determines