Simulation of cycles in the IEH graph

The Incrementally Extensible Hypercube (IEH) is a novel interconnection net work derived from the hypercube. Unlike the hypercube, the IEH graph is inc rementally extensible, that is, it can be constructed for any number of nod es. In addition, it has optimal fault tolerance and its diameter is logarit hmic in the number of nodes and the difference of the maximum and the minim um degree of a node in the graph is less than or equal to 1 (i.e., the grap h is almost regular). In this paper, we show that almost the entire IEH gra ph, except for those with N = 2(n) - 1 nodes for all n greater than or equa l to 2, has a Hamiltonian cycle; if an IEH graph has N = 2(n) - 1 nodes the n it has only a Hamiltonian path, not cycle. These results enable us to obt ain the good embedding of rings and linear arrays into the IEH graph.