Fault-tolerant Pancyclicity of Twisted Cubes
Jun‐Ming Xu · Yunchou yu guanli · 2007
Containing cycles of all possible lengths in an interconnection network is an important topological property.The twisted cube TQn is a variant of the hypercube Qn,where n is an odd larger than one.Chang et al [Information Science,113(1999),147-167] proved that TQn contains all cycles of length from 4 to 2n.Huang et al.[J.Parallel and Distributed Computing,62(2002),591-640] proved that TQn contains a cycle of length 2n-fv if the sum of faulty vertices and faulty edges is not more than(n-2),where fv is the number of faultyvertices.This note improves these results as that TQn contains all cycles of length from 4 to 2n-fv.This result is optimal.