Weakly Edge-Pancyclicity of Locally Twisted Cubes

Meijie Ma1, Jun-Ming Xu2
1Department of Mathematics, Zhejiang Normal University Jinhua, 321004, China
2Department of Mathematics, University of Science and Technology of China Hefei, 230026, China

Abstract

The locally twisted cube \(LTQ_n\) is a newly introduced interconnection network for parallel computing. As a variant of the hypercube \(Q_n\), \(LTQ_n\) 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 \(LTQ_n\) contains a cycle of every length from \(4\) to \(2^n\). In this note, we improve this result by showing that every edge of \(LTQ_n\) lies on a cycle of every length from \(4\) to \(2^n\) inclusive.