Cyclic connectivity of the data center network.

Let G be a connected graph, F be a subset of V (G) , S be a subset of E (G). The cyclic vertex connectivity of G, denoted by κ c (G) , is the minimum cardinality of F such that G−F is disconnected and at least two of its components contain cycles. The cyclic edge connectivity of G, denoted by λ c (G) , is the minimum cardinality of S such that G−S is disconnected and at least two of its components contain cycles. Let D k , n denote the data center network. In this paper, we obtain the following results: κ c (D k , 2) = 6 k − 6 for k ≥ 2 ; κ c (D k , n) = n + 3 k − 3 for k ≥ 2 , n ≥ 3 ; λ c (D k , 2) = 6 k − 6 for k ≥ 2 ; λ c (D 2 , n) = 2 n for n ≥ 3 ; λ c (D k , n) = 3 n + 3 k − 9 for k ≥ 3 , n ≥ 3. [ABSTRACT FROM AUTHOR]