Hamiltonicity of matching composition networks with conditional edge faults

Abstract

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. © 2008 Springer-Verlag Berlin Heidelberg.