Weakly Edge-Pancyclicity of Locally Twisted Cubes

Abstract

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