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), ...