Cycles in folded hypercubes

This work investigates important properties related to cycles of embedding into the folded hypercube FQ(n) for n >= 2. The authors observe that FQ(n) is bipartite if and only if n is odd, and show that the minimum length of odd cycles is n + 1 if n is even. The authors further show that every edge of FQ(n) lies on a cycle of every even length from 4 to 2(n); if n is even, every edge of FQ(n) also lies on a cycle of every odd length from n + 1 to 2(n) - 1. (C) 2005 Elsevier Ltd. All rights reserved.