Processor (vertex) faults and link (edge) faults may happen when a network is used, and it is meaningful to consider networks (graphs) with faulty processors and/or links. A k-regular Hamiltonian and Hamiltonian connected graph G is optimal fault-tolerant Hamiltonian and Hamiltonian connected if G remains Hamiltonian after removing at most k-2 vertices and/or edges and remains Hamiltonian connected after removing at most k-3 vertices and/or edges. In this paper, we investigate in constructing optimal fault-tolerant Hamiltonian and optimal fault-tolerant Hamiltonian connected graphs. Therefore, some of the generalized hypercubes, twisted-cubes, crossed-cubes, and Mobius cubes are optimal fault-tolerant Hamiltonian and optimal fault-tolerant Hamiltonian connected.
- Hamiltonian connectivity
- Generalized hypercube
Chen, Y-C., Huang, Y-Z., Hsu, L-H., & Tan, J-M. (2010). A family of Hamiltonian and Hamiltonian connected graphs with fault tolerance. Journal of Supercomputing, 54(2), 229-238. https://doi.org/10.1007/s11227-009-0316-3