具有故障边的二维环面网络的哈密尔顿路Hamiltonian Path of a Two-dimensional Torus Network with Fault Edges
张建秀,李晶,田小润
摘要(Abstract)：
二维环面是一类重要的互连网络,被广泛应用到当前大型分布式系统的网络拓扑中。研究具有故障边的二维环面网络Torus(m,n)上的哈密尔顿路问题,并证明了以下结论:(1)设F是二部图环网Torus(m,n)(m,n≥4是偶数)的故障边集,u和v是不同部中的两个顶点。若|F|≤4,u为Torus(m,n)-F中的唯一1度顶点且(u,v)?E(Torus(m,n)-F),则Torus(m,n)-F中存在哈密尔顿路连接u和v.(2)设F是环网Torus(m,n)(m,n≥6是偶数)的故障边集。若|F|≤5,u为Torus(m,n)-F中的唯一1度顶点,则点u至少有两个邻点与u之间有哈密尔顿路,并且这些邻点与u以故障边在Torus(m,n)中连接。
关键词(KeyWords)： 互连网络;二维环面;容错问题;哈密尔顿路
基金项目(Foundation): 国家自然科学基金(11701406);; 山西省回国留学人员科研资助基金(2020-122)
作者(Author): 张建秀,李晶,田小润
参考文献(References)：
- [1]李晶．Torus网络的容错性[M]．西安:西安交通大学出版社，2017.
- [2] KIM HEE-CHUL,PARK JUNG-HEUM. Fault hamiltonicity of two-dimensional torus networks[C]∥Proc. of Workshop on Algorithms and Computation WAAC00,2000:110-117.
- [3] PARK JUNG-HEUM,KIM HEE-CHUL. Fault-hamiltonicity of product graph of path and cycle[J]. Proceedings of the 9th annual international conference on Computing and combinatorics,Springer-Verlag Berlin,Heidelberg,2003:319-328.
- [4] XIANG YONG-HONG,STEWART IAIN-A. Bipancyclicity in k-ary n-cube with faulty edges under a conditional fault assumption[J]. IEEE Transactions on Parallel and Distributed Systems,2011,22(9):1506-1513.
- [5] LI JING,YANG YUXING,GAO XIAOHUI. Hamiltonicity of the torus network under the conditional fault model[J]. International Journal of Foundations of Computer Science,World Scientific Publishing Company,2017:211-227.
- [6] JANUSZ DYBIZBA ■,ANDRZEJ SZEPIETOWSKI. Hamiltonian paths in hypercubes with local traps[J]. Institute of Informatics,Information Sciences,2017(45):258-270.