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

Abstract

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 FCCN(n) to denote the fully connected cubic network of level n. Let G = (V, E) be a graph. The fault-tolerant hamiltonian connectivity H(f)(k) (G) is defined to be the maximum integer l such that G - F remains hamiltonian connected for every F subset of V(G) boolean OR E(G) with vertical bar F vertical bar <= l. The fault-tolerant hamiltonicitly H(f)(G) is defined to be the maximum integer l such that G - F remains hamiltonian for every F subset of V(G) boolean OR E(G) with vertical bar F vertical bar <= l. We prove that H(f)(k) (FCCN(n)) = 0 and H(f)(FCCN(n)) = 1 if n >= 2.