Fault-Tolerant Hamiltonian Connectivity of DPCell

Interconnection networks are critical components in the design of parallel and distributed systems. Given that node or edge failures are inevitable in large-scale networks, investigating the Hamiltonicity of faulty networks becomes essential. Robust fault tolerance can significantly enhance the design of routing algorithms and improve network communication. DPCell is a highly scalable network structure, however, there is no research on its fault-tolerant Hamiltonicity. In this paper, we explore the fault-tolerant Hamiltonicity of DPCell from a graph-theoretic perspective. We demonstrate that an r-layer DPCell is <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Sigma_{i=0}^{r}k_{i}$</tex>- 2-fault Hamiltonian and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\Sigma_{i=0}^{r}k_{i}-3$</tex> -fault Hamiltonian-connected for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k_{\mathrm{i}}\geq 1$</tex>.