Finding Hamiltonian cycles on incrementally extensible hypercube graphs

The existence of a Hamiltonian cycle is the premise of usage in an interconnection network. A novel interconnection network, the incrementally extensible hypercube (IEH) graph, has been proposed. The IEH graphs are derived from hypercubes and also retain most of the properties of hypercubes. Unlike hypercubes without incremental 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 IEH graphs except for those containing exactly 2ⁿ-1 nodes