Abstract:SUMMARYIn this paper, we investigate the fault-tolerant Hamiltonian problems of crossed cubes with a faulty path. More precisely, let P denote any path in an n-dimensional crossed cube CQ n for n ≥ 5, and let V(P) be the vertex set of P. We show that CQ n − V(P) is Hamiltonian if |V(P)| ≤ n and is Hamiltonian connected if |V(P)| ≤ n−1. Compared with the previous results showing that the crossed cube is (n − 2)-fault-tolerant Hamiltonian and (n − 3)-fault-tolerant Hamiltonian connected for arbitrary faults, the… Show more
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.