Fault-Hamiltonicity of Product Graph of Path and Cycle

We investigate hamiltonian properties of Pm × Cn, m ≥ 2 and even n ≥ 4, which is bipartite, in the presence of faulty vertices and/or edges. We show that Pm×Cn with n even is strongly hamiltonianlaceable 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 Pm × Cn to a two-dimensional torus Cm × Cn, we obtain interesting hamiltonian properties of a faulty Cm × Cn.

• Type: Conference
• Year: 2003
• Where: COCOON
• Authors: Jung-Heum Park, Hee-Chul Kim
• Keywords: COCOON 2003, Faulty Elements, Faulty Vertices, Hamiltonian Properties