Hamiltonicity of Matching Composition Networks with Conditional Edge Faults

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In this paper, we sketch structure characterization of a class of networks, called Matching Composition Networks (MCNs), to establish necessary conditions for determining the conditional fault hamiltonicity. We then apply our result to n-dimensional restricted hypercube-like networks, including n-dimensional crossed cubes, and n-dimensional locally twisted cubes, to show that there exists a fault-free Hamiltonian cycle if there are at most 2n − 5 faulty edges in which each node is incident to at least two fault-free edges. We also demonstrate that our result is worst-case optimal with respect to the number of faulty edges tolerated.