Cyclic connectivity of the data center network. Issue 6 (2nd November 2021)

• Record Type: Journal Article
• Authors: Zhu, Hongzhou; Meng, Jixiang
• Is Part Of: International journal of parallel, emergent and distributed systems. Volume 36:Issue 6(2021)
• Page Start: 623
• Page End: 629
• Publication Date: 2021-11-02
• Subjects: Cyclic vertex connectivity -- cyclic edge connectivity -- data center network; Parallel computers -- Periodicals; Electronic data processing -- Distributed processing -- Periodicals; Computer algorithms -- Periodicals; 004.35
• DOI: 10.1080/17445760.2021.1952579
• Languages: English
• ISSNs: 1744-5760

Abstract

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 .