摘要
互连网络包含所有可能长度的圈是一个重要的拓扑性质。纽立方体网络TOn是超立方体网络Qn的一种变型,其中n≥3是奇数。Chang等人[Information Science,113(1999),147-167]证明了TOn中包含任意长度为l的圈,其中4≤l≤2n。如果TOn中的故障点数和故障边数之和不超过(n-2),Huang等人[J.Parallel andDistributed Computing,62(2002),591-640]证明了:TQn中包含长度为2n-fv的圈,其中fv是故障点数。这篇文章改进这些结果为:TQn中包含任意长度为l的圈,其中4≤l≤2n-fv。
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）, 147-1673 proved that TQn contains all cycles of length from 4 to 2n. Huang et al. [J. Parallel and Distributed Computing, 62（2002）, 591-6403 proved that TQn contains a cycle of length 2^n-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 2^n-fv. This result is optimal.
出处
《运筹与管理》
CSCD
2007年第1期52-57,共6页
Operations Research and Management Science
基金
国家自然科学基金资助项目
关键词
应用数学
图论
网络
容错泛圈
纽立方体网络
applied mathematics
graph theory
networks
fault-tolerant pancyclicity
twisted cubes.
