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Conditional Edge-Fault Hamiltonicity of Matching Composition Networks

机译：匹配组合网络的条件边缘故障哈密顿性

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摘要

A graph G is called Hamiltonian if there is a Hamiltonian cycle in G. The conditional edge-fault Hamiltonicity of a Hamiltonian graph G is the largest k such that after removing k faulty edges from G, provided that each node is incident to at least two fault-free edges, the resulting graph contains a Hamiltonian cycle. In this paper, we sketch common properties of a class of networks, called matching composition networks (MCNs), such that the conditional edge-fault hamiltonicity of MCNs can be determined from the found properties. We then apply our technical theorems to determine conditional edge-fault hamiltonicities of several multiprocessor systems, including n-dimensional crossed cubes, n-dimensional twisted cubes, n-dimensional locally twisted cubes, n-dimensional generalized twisted cubes, and n-dimensional hyper Petersen networks. Moreover, we also demonstrate that our technical theorems can be applied to network construction.
机译：如果G中存在哈密顿循环，则图G称为哈密顿量。哈密顿图G的条件边缘故障哈密顿性是最大的k，使得从G去除k个有缺陷的边后，只要每个节点都入射到至少两个无故障边缘，结果图包含哈密顿循环。在本文中，我们草绘了一类称为匹配组合网络（MCN）的网络的公共属性，以便可以从发现的属性中确定MCN的条件边缘故障哈密尔顿性。然后，我们使用技术定理确定几种多处理器系统的条件边缘故障半咸性，包括n维交叉立方体，n维扭曲立方体，n维局部扭曲立方体，n维广义扭曲立方体和n维超扭曲彼得森网络。此外，我们还证明了我们的技术定理可以应用于网络建设。

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