Fault-Tolerant Hamiltonian Connectivity and Fault-Tolerant Hamiltonicity of the Fully Connected Cubic Networks

Many papers on the fully connected cubic networks have been published for the past several years due to its favorite properties. In this paper, we consider the fault-tolerant hamiltonian connectivity and fault-tolerant hamiltonicity of the fully connected cubic network. We use FCCNn to denote the fully connected cubic network of level n. Let G = (V, E) be a graph. The fault-tolerant hamiltonian connectivity H f (G) is defined to be the maximum integer l such that G − F remains hamiltonian connected for every F ⊂ V(G) ∪ E(G) with |F| ≤ l. The fault-tolerant hamiltonicity Hf (G) is defined to be the maximum integer l such that G − F remains hamiltonian for every F ⊂ V(G) ∪ E(G) with |F| ≤ l. We prove that H f (FCCNn) = 0 and Hf (FCCNn) = 1 if n ≥ 2.