Rigidity properties of the hypercube via Bakry–Émery curvature

Abstract We give rigidity results for the discrete Bonnet–Myers diameter bound and Lichnerowicz eigenvalue estimate. Both inequalities are sharp if only underlying graph is a hypercube. The proofs use well-known semigroup methods as well new direct which translate curvature to combinatorial properties. Our can be seen first known analogues of Cheng’s Obata’s theorems.