Finding Hamiltonian cycles on incrementally extensible hypercube graphs

The existence of a Hamiltonian cycle is the premise of usages in an interconnection network. A novel interconnection network, the incrementally Extensible Hypercube (IEH) graph, has been proposed recently. The IEH graphs are derived from hypercubes and also retain most parts of properties in hypercubes. Unlike hypercubes without incrementally extensibility, IEH graphs can be constructed in any number of nodes. In this paper, we present an algorithm to find a Hamiltonian cycle or path and prove that there exists a Hamiltonian cycle in all of IEH graphs except for those containing exactly 2(n)-1 nodes.