@article{Wang2020, 
author = {Gui-Juan Wang and Cheng-Kuan Lin and Jian-Xi Fan and Jing-Ya Zhou and Bao-Lei Cheng},
title = {Fault-Tolerant Hamiltonicity and Hamiltonian Connectivity of BCube with Various Faulty Elements},
year = {2020},
journal = {Journal of Computer Science and Technology},
volume = {35},
number = {5},
pages = {1064-1083},
keywords = {data center network, BCube, fault-tolerance, Hamiltonicity, Hamiltonian connectivity},
url = {https://www.sciopen.com/article/10.1007/s11390-020-9508-3},
doi = {10.1007/s11390-020-9508-3},
abstract = {BCube is one kind of important data center networks. Hamiltonicity and Hamiltonian connectivity have significant applications in communication networks. So far, there have been many results concerning fault-tolerant Hamiltonicity and fault-tolerant Hamiltonian connectivity in some data center networks. However, these results only consider faulty edges and faulty servers. In this paper, we study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity of BCube(n,k) under considering faulty servers, faulty links/edges, and faulty switches. For any integers n ≥ 2 and k ≥ 0, let BCn,k be the logic structure of BCube(n,k) and F be the union of faulty elements of BCn,k. Let fv, fe, and fs be the number of faulty servers, faulty edges, and faulty switches of BCube(n,k), respectively. We show that BCn,k − F is fault-tolerant Hamiltonian if fv +fe + (n − 1)fs ≤ (n − 1)(k + 1) − 2 and BCn,k −F is fault-tolerant Hamiltonian-connected if fv + fe + (n − 1)fs ≤ (n − 1)(k + 1) − 3. To the best of our knowledge, this paper is the first work which takes faulty switches into account to study the fault-tolerant Hamiltonicity and the fault-tolerant Hamiltonian connectivity in data center networks.}
}