@article{Zhu2023, 
author = {Bo Zhu and Shumin Zhang and Jinyu Zou and Chengfu Ye},
title = {Structure connectivity and substructure connectivity of data center network},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {4},
pages = {9877-9889},
keywords = {structure connectivity, substructure connectivity, data center network},
url = {https://www.sciopen.com/article/10.3934/math.2023499},
doi = {10.3934/math.2023499},
abstract = {The structure connectivity    κ  (  G  ;  H  ) and substructure connectivity        κ    s    (  G  ;  H  ) are important indicators to measure interconnection network's fault tolerance and reliability. The data center network, denoted by        D          k      ,      n      , have been proposed for data centers as a server-centric interconnection network structure, which can support millions of servers with high network capacity by only using commodity switches. In this paper, we obtain    κ  (      D          k      ,      n        ;      S    m    ) and        κ    s    (      D          k      ,      n        ;      S    m    ) when    k  ≥  2,    n  ≥  4 and    1  ≤  m  ≤  n  +  k  −  2. Furthermore, we obtain both    κ  (      D          k      ,      n        ;      S          23        ) and        κ    s    (      D          k      ,      n        ;      S          23        ) for    k  ≥  8 and    n  ≥  8.}
}