We give rigidity results for discrete Bonnet-Myers diameter boundand Lichnerowicz eigenvalue estimate. Both inequalities are sharp ifand only if the underlying graph is a hypercube.  The proofs usewell-known semigoup methods as well as new direct methods whichtranslate curvature to combinatorial properties.  The results can beseen as first known discrete analogues of Cheng'sand Obata's rigidity theorems.

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