The [formula omitted]-restricted edge-connectivity of the data center network DCell.

• The design of DCNs represented by DCell networks is a hot research topic. DCell is an excellent network performing by using a large number of servers and inexpensive commodity switches. As a server-centric DCN, DCell has many desirable features. • The concept of k -restricted edge-connectivity proposed by Fábrega and Foil has been applied successfully in the further study of fault tolerance and reliability of networks. • For any integers m ≥ 0 and n ≥ 2 , we use D m , n to denote the m-dimensional DCell with n -port switches. We completely determine the k-restricted edge-connectivity of D m , n and we also characterize the structure of the minimum λ k -cuts of D m , n for 2 ≤ k ≤ n. For any integers m ≥ 0 and n ≥ 2 , we use D m , n to denote the m -dimensional DCell with n -port switches. For a simple graph G = (V , E) , an edge subset S ⊂ E (G) is said to be a λ k -cut of G , if G − S is disconnected and each component of G − S has at least k vertices. The k -restricted edge-connectivity of G , denoted by λ k (G) , is the minimum cardinality of all λ k -cuts of G. We prove that λ k (D m , n) = k (m + n − k) for m ≥ n ≥ 2 and 2 ≤ k ≤ n , λ k (D m , n) = m n for n > m ≥ 2 and m ≤ k ≤ n and λ k (D m , n) = k (m + n − k) for n > m ≥ 2 and 2 ≤ k < m. We also characterize the structure of the minimum λ k -cuts of D m , n in terms of the above conclusions. [ABSTRACT FROM AUTHOR]