The Hamiltonicity of Crossed Cubes in the Presence of Faults

The crossed cube is considered as one of the most promising variations of the hypercube topology, due to its ability of preserving many of the attractive properties of the hypercube and reducing the diameter by a factor of two. In this paper, we show the robustness capability of the crossed cube in constructing a Hamiltonian circuit despite the presence of faulty nodes or edges. Our result is optimal in the fact that it constructs the Hamiltonian circuit by avoiding only faulty nodes and edges in a crossed hypercube of dimension n. Our algorithm can tolerate up to 2(n-3) faults with the restriction that each sub cube CQ(3) has at most one faulty node.