Weakly Edge-Pancyclicity of Locally Twisted Cubes

The locally twisted cube LTQn is a newly introduced interconnection network for parallel computing. As a variant of the hypercube Qn, LTQn has better properties than Qn with the same number of links and processors. Yang, Megson and Evans [Locally twisted cubes are 4pancyclic, Applied Mathematics Letters, 17 (2004), 919-925] showed that LTQn contains a cycle of every length from 4 to 2 . In this note, we improve this result by showing that every edge of LTQn lies on a cycle of every length from 4 to 2 inclusive.