A tight bound on {C_3,C_5}-free connected graphs with positive Lin-Lu-Yau Ricci curvature

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 2^2/κ. This upper bound is achieved if and only if G is a hypercube Q_d and κ=2/d for some integer d≥ 1.