## Abstract

DCell has been proposed for data centers as a server-centric interconnection network structure. DCell can support millions of servers with high network capacity by only using commodity switches. With one exception, we prove that a $$k$$ level DCell built with $$n$$ port switches is Hamiltonian-connected for $$k \geq 0$$ and $$n \geq 2$$. Our proof extends to all Generalized DCell connection rules for $$n\ge 3$$. Then, we propose an $$O(t_k)$$ algorithm for finding a Hamiltonian path in $$DCell_{k}$$, where $$t_k$$ is the number of servers in $$DCell_{k}$$. Furthermore, we prove that $$DCell_{k}$$ is $$(n +k - 4)$$-fault Hamiltonian-connected and $$(n +k - 3)$$-fault Hamiltonian. In addition, we show that a partial DCell is Hamiltonian-connected if it conforms to a few practical restrictions.