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Conditional Edge-Fault Hamiltonicity of Cartesian Product Graphs

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3 Author(s)
Chia-Wen Cheng ; National Cheng Kung University, Tainan ; Chia-Wei Lee ; Sun-Yuan Hsieh

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 x 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.

Published in:

IEEE Transactions on Parallel and Distributed Systems  (Volume:24 ,  Issue: 10 )