Cycles in folded hypercubes Original Research Article

This work investigates important properties related to cycles of embedding into the folded hypercube View the MathML sourceFQn for n≥2n≥2. The authors observe that View the MathML sourceFQn is bipartite if and only if nn is odd, and show that the minimum length of odd cycles is n+1n+1 if nn is even. The authors further show that every edge of View the MathML sourceFQn lies on a cycle of every even length from 4 to 2n2n; if nn is even, every edge of View the MathML sourceFQn also lies on a cycle of every odd length from n+1n+1 to 2n−12n−1.