Abstract
We consider the fault hamiltonian properties of m× n meshes with two wraparound edges in the first row and the last row, denoted by M 2(m,n), m ≥ 2, n ≥ 3. M 2(m,n) is a spanning subgraph of P m × C n which has interesting fault hamiltonian properties. We show that M 2(m,n) with odd n is hamiltonian-connected and 1-fault hamiltonian. For even n, M 2(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 P m × C n 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 M 2(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.
This work was supported by grant No. R01-2003-000-11676-0 from the Basic Research Program of the Korea Science & Engineering Foundation.
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Park, KW., Lim, HS., Park, JH., Kim, HC. (2004). Fault Hamiltonicity of Meshes with Two Wraparound Edges. In: Chwa, KY., Munro, J.I.J. (eds) Computing and Combinatorics. COCOON 2004. Lecture Notes in Computer Science, vol 3106. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27798-9_44
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DOI: https://doi.org/10.1007/978-3-540-27798-9_44
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