Hamiltonian Connectivity of Twisted Hypercube-Like Networks under the Large Fault Model

Details Hamiltonian Connectivity of Twisted Hypercube-Like Networks under the Large Fault Model Hamiltonian Connectivity of Twisted Hypercube-Like Networks under the Large Fault Model

2011-11-23

arxiv.org/abs/1111.5391v1

Computer Science

Distributed, Parallel, and Cluster Computing

22 pages, 26 figures, Submitted to IEEE TPDS

Scientific paper

Twisted hypercube-like networks (THLNs) are an important class of interconnection networks for parallel computing systems, which include most popular variants of the hypercubes, such as crossed cubes, M\"obius cubes, twisted cubes and locally twisted cubes. This paper deals with the fault-tolerant hamiltonian connectivity of THLNs under the large fault model. Let $G$ be an $n$-dimensional THLN and $F \subseteq V(G)\bigcup E(G)$, where $n \geq 7$ and $|F| \leq 2n - 10$. We prove that for any two nodes $u,v \in V(G - F)$ satisfying a simple necessary condition on neighbors of $u$ and $v$, there exists a hamiltonian or near-hamiltonian path between $u$ and $v$ in $G-F$. The result extends further the fault-tolerant graph embedding capability of THLNs.

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