Fault Hamiltonicity of Meshes with Two Wraparound Edges [chapter]

Kyoung-Wook Park, Hyeong-Seok Lim, Jung-Heum Park, Hee-Chul Kim
2004 Lecture Notes in Computer Science  
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 × Cn 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, 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
more » ... hown 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 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.
doi:10.1007/978-3-540-27798-9_44 fatcat:lrmkq4pg7vadxgb2z4jkgdpc5a