Hamiltonian properties of twisted hypercube-like networks with more faulty elements

• Published in: Theoretical computer science Vol. 412; no. 22; pp. 2409 - 2417
• Main Authors: Yang, Xiaofan, Dong, Qiang, Yang, Erjie, Cao, Jianqiu
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 13.05.2011; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Computer systems performance. Reliability; Exact sciences and technology; Fault tolerance; Hamiltonian cycle; Hypercubes; Interconnection networks; Miscellaneous; Near Hamiltonian cycle; Networks; Software; Theoretical computing; Topology; Twisted hypercube-like network; Fault tolerance; Near Hamiltonian cycle; Twisted hypercube-like network; Hamiltonian cycle; Interconnection networks; Interconnection network; Network topology; Fault tolerant computing; Computer theory; Hypercube; Hamiltonian
• ISSN: 0304-3975; 1879-2294
• DOI: 10.1016/j.tcs.2011.01.034

Twisted hypercube-like networks (THLNs) are a large class of network topologies, which subsume some well-known hypercube variants. This paper is concerned with the longest cycle in an n -dimensional ( n -D) THLN with up to 2 n − 9 faulty elements. Let G be an n -D THLN, n ≥ 7 . Let F be a subset of V ( G ) ⋃ E ( G ) , | F | ≤ 2 n − 9 . We prove that G − F contains a Hamiltonian cycle if δ ( G − F ) ≥ 2 , and G − F contains a near Hamiltonian cycle if δ ( G − F ) ≤ 1 . Our work extends some previously known results.