Linearity of graph products

In this work we prove that, given a simplicial graph Γ $\Gamma$ and family G $\mathcal {G}$ of linear groups over domain R $R$ , the product $\Gamma \mathcal is [ t ̲ ] $R[\underline{t}]$ where $\underline{t}$ tuple finitely many linearly independent variables. As consequence, obtain that any complex numbers again group numbers. This solves an open problem Hsu Wise (Michigan Math. J. 46 (1999), no. 2, 251–259, Problem 1, p. 258) in case faithful representations C $\mathbb {C}$ .