Let G be a group, and $${{\,\mathrm{Sol}\,}}(G)=\{x \in : \langle x,y \rangle \text { is solvable for all } y G\}$$ . We associate graph $$\mathcal {NS}_G$$ (called the non-solvable of G) with whose vertex set $$G \setminus {{\,\mathrm{Sol}\,}}(G)$$ two distinct vertices are adjacent if they generate subgroup. In this paper, we study many properties particular, obtain results on degree, cardina...