Fault Hamiltonicity Of Meshes With Two Wraparound Edges

We consider the fault hamiltonian properties of m x n meshes with two wraparound edges in the first row and the last row, denoted by M-2 (m, n), m greater than or equal to 2, n greater than or equal to 3. M-2 (m, n) is a spanning subgraph of P-m x 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 x C-n also has these hamiltonian properties. Our result shows that two additional wraparound edges are sufficient for an m x 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.