Cyclic connectivity of the data center network. Issue 6 (2nd November 2021) - Zhu, Hongzhou; Meng, Jixiang
Abstract : 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 .