Conditional edge-fault hamiltonicity of cartesian product graphs

A graph (G) is conditional (k)-edge-fault Hamiltonian if it remains Hamiltonian after deleting at most (k) edges and each vertex incident to at least two nonfaulty edges. A graph (G) is (k)-edge-fault Hamiltonian-connected if it remains Hamiltonian-connected after deleting at most (k) edges. This study shows that the conditional edge-fault Hamiltonicity of the Cartesian product network (G\times H) can be efficiently evaluated given two graphs (G) and (H) that are edge-fault Hamilton-connected and conditional edge-fault Hamiltonian. This study uses the result to evaluate the conditional edge-fault Hamiltonicity of two multiprocessor systems, the generalized hypercubes and the nearest neighbor mesh hypercubes, both of which belong to Cartesian product networks.