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COCOON
2004
Springer

Fault Hamiltonicity of Meshes with Two Wraparound Edges

13 years 9 months ago
Fault Hamiltonicity of Meshes with Two Wraparound Edges
We consider the fault hamiltonian properties of m×n meshes with two wraparound edges in the first row and the last row, denoted by M2(m, n), m ≥ 2, n ≥ 3. M2(m, n) is a spanning subgraph of Pm × Cn which has interesting fault hamiltonian properties. We show that M2(m, n) with odd n is hamiltonian-connected and 1-fault hamiltonian. For even n, M2(m, n), which is bipartite, with a single faulty element is shown to be 1-fault strongly hamiltonian-laceable. In previous works[1, 2], it was shown that Pm ×Cn also has these hamiltonian properties. Our result shows that two additional wraparound edges are sufficient for an m × n mesh to have such properties rather than m wraparound edges. As an application of fault-hamiltonicity of M2(m, n), we show that the n-dimensional hypercube is strongly hamiltonian laceable if there are at most n − 2 faulty elements and at most one faulty vertex.
Kyoung-Wook Park, Hyeong-Seok Lim, Jung-Heum Park,
Added 01 Jul 2010
Updated 01 Jul 2010
Type Conference
Year 2004
Where COCOON
Authors Kyoung-Wook Park, Hyeong-Seok Lim, Jung-Heum Park, Hee-Chul Kim
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