Fault-tolerant hamiltonicity and fault-tolerant hamiltonian connectivity of the folded Petersen cube networks

Some research on the folded Petersen cube networks have been published for the past several years due to its favourite properties. In this paper, we consider the fault-tolerant hamiltonicity and the fault-tolerant hamiltonian connectivity of the folded Petersen cube networks. We use FPQn, k to denote the folded Petersen cube networks of parameters n and k. In this paper, we show that FPQn, k-F remains hamiltonian for any F V(FPQn, k)E(FPQn, k) with |F|n+3k-2 and FPQn, k-F remains hamiltonian connected for any F V(FPQn, k)E(FPQn, k) with |F|n+3k-3 if (n, k){(0, 1)}{(n, 0) | n is a positive integer}. Moreover, this result is optimal.