Embedding of cycles in twisted cubes with edge-pancyclic

In this paper, we study the embedding of cycles in twisted cubes. It has been proven in the literature that, for any integer l, 4 ≤ l ≤ 2 ⁿ , a cycle of length l can be embedded with dilation 1 in an n-dimensional twisted cube, n ≥ 3. We obtain a stronger result of embedding of cycles with edge-pancyclic. We prove that, for any integer l, 4 ≤ l ≤ 2 ⁿ , and a given edge (x,y) in an n-dimensional twisted cube, n ≥ 3, a cycle C of length l can be embedded with dilation 1 in the n-dimensional twisted cube such that (x,y) is in C in the twisted cube. Based on the proof of the edge-pancyclicity of twisted cubes, we further provide an O(llog∈l+n ²+nl) algorithm to find a cycle C of length l that contains (u,v) in TQ _n for any (u,v) E(TQ _n ) and any integer l with 4 ≤ l ≤ 2 ⁿ. © 2007 Springer Science+Business Media, LLC.