Simulation of Cycles in the IEH Graph

Abstract

The Incrementally Extensible Hypercube (IEH) is a novel interconnection network derived from the hypercube. Unlike the hypercube, the IEH graph is incrementally extensible, that is, it can be constructed for any number of nodes. In addition, it has optimal fault tolerance and its diameter is logarithmic in the number of nodes and the difference of the maximum and the minimum degree of a node in the graph is (i.e., the graph is almost regular). In this paper, we show that almost the entire IEH graph, except for those with N =2n-1 nodes for all , has a Hamiltonian cycle; if an IEH graph has N=2n-1 nodes then it has only a Hamiltonian path, not cycle. These results enable us to obtain the good embedding of rings and linear arrays into the IEH graph.