<s>[INST] For the ckass $\mathscr{C}$ of all connected simple graphs with $n\ge 3$ vertices, define a parameter $p(G)=\min \{d_G(v)\mid v\in V(G)\}$. Prove that there exists an absolute constant $c>0$ such that $|\mathscr{C}|> (1+c)^n$ for all sufficiently large $n$.[/INST]