Fault-Hamiltonicity Of Product Graph Of Path And Cycle

We investigate hamiltonian properties of P-m x C-n, m greater than or equal to 2 and even n greater than or equal to 4, which is bipartite, in the presence of faulty vertices and/or edges. We show that P-m X C-n with n even is strongly hamiltonian-laceable if the number of faulty elements is one or less. When the number of faulty elements is two, it has a fault-free cycle of length at least mn - 2 unless both faulty elements are contained in the same partite vertex set; otherwise, it has a fault-free cycle of length mn - 4. A sufficient condition is derived for the graph with two faulty edges to have a hamiltonian cycle. By applying fault-hamiltonicity of P-m x C-n to a two-dimensional torus C-m x C-n, we obtain interesting hamiltonian properties of a faulty C-m X C-n.