Structure connectivity and substructure connectivity of data center network

Abstract

<abstract><p>The structure connectivity $ \kappa(G; H) $ and substructure connectivity $ \kappa^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 $ \kappa(D_{k, n}; S_m) $ and $ \kappa^s(D_{k, n}; S_m) $ when $ k\geq2 $, $ n\geq4 $ and $ 1\leq m\leq n+k-2 $. Furthermore, we obtain both $ \kappa(D_{k, n}; S_{23}) $ and $ \kappa^s(D_{k, n}; S_{23}) $ for $ k\geq8 $ and $ n\geq8 $.</p></abstract>