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 FQn is bipartite if and only if n is odd, and show that the minimum length of odd cycles is n + 1i fn is even. The authors further show that every edge of FQn lies on a cycle of every even length from 4 to 2 n ;i fn is even, every edge of FQn also lies on a cycle of every odd length from n + 1t o 2 n − 1.