Embedding cycles in IEH graphs

Abstract

We embed cycles into IEH graphs. First, IEH graphs are proved to be Hamiltonian except when they are of size 2(n) -1 for all n greater than or equal to 2. Next, we show that for an IEH graph of size N, an arbitrary cycle of even length N-e where 3 < N-e < N is found. We also find an arbitrary cycle of odd length N-o where 2 < N-o < N if and only if a node of this graph has at least one forward 2-Inter-Cube (IC) edges. These results help describe the whole cycle structure in IEH graphs. (C) 1997 Elsevier Science B.V.