Fault-Tolerant Hamiltonian Connectivity and Fault-Tolerant Hamiltonicity of the Fully Connected Cubic Networks
Tung-Yang Ho, Cheng‐Kuan Lin · 2009
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-tol- erant 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 k 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 k f (FCCNn) = 0 and Hf (FCCNn) = 1 if n ≥ 2.