Abstract: Shannon capacity (also called Channel capacity) was introduced by C.E. Shannon in 1956 to measure the rate of information that can be reliably transmitted over a commutations channel and gained attentions from well-known mathematicians as L. Lovász and N. Alon. However, until now, almost problems on Shannon capacity is sill open. In the first part this talk, I will introduce about zero error Shannon capacity: definitions, some classical results, applications. In the second part, I will present my new improvements on the upper bound on the Shannon capacity of cycle graphs, and some open problems.