Cycles in folded hypercubes (Q2488687)

From the authors' abstract: This work investigates important properties related to cycles of embedding into the folded hypercube \(\text{FQ}_n\) for \(n \geq 2\). The authors observe that \(\text{FQ}_n\) 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 \(\text{FQ}_n\) lies on a cycle of every even length from 4 to \(2^n\); if \(n\) is even, every edge of \(\text{FQ}_n\) also lies on a cycle of every odd length from \(n+1\) to \(2^n-1\).