报告摘要：
| The Bonnet-Myers theorem states that an n-dimenisonal complete Riemannian manifold M with Ricci curvature lower bounded by a positive number (n-1)K is compact, and its diameter is no greater than $pi/sqrt{K}$ . Moreover, Cheng's rigidity theorem tells that the diameter estimate is sharp if and only if M is the n-dimensional round sphere. Recently, discrete Bonnet-Myers theorems have been established with respect to two types of discrete Ricci curvature, that is, the Ollivier Ricci curvature modified by Lin, Lu, and Yau and the Bakry-Emery curvature. This enables us to explore the discrete analogues of round spheres in graph theory via exploring the corresponding rigidity results. I will present two discrete Cheng type rigidity results. In fact, the discrete analogues of spheres in this sense coincide much with the so-called (strongly) spherical graphs introduced in graphs theory in 2003 as generalizations of hypercubes.
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