In this paper, we prove that any simple $\{C_3,C_5\}$-free non-empty connected graph $G$ with LLY curvature bounded below by $κ>0$ has the order at most $2^{\frac{2}κ}$. This upper bound is achieved if and only if $G$ is a hypercube $Q_d$ and $κ=\frac{2}{d}$ for some integer $d\geq 1$.
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