条件故障下k-元n-立方体的强Menger边连通度  

Strong Menger Edge Connectivity of k-ary n-cubes under Conditional Faults

作　　者：秦学姣[1] QIN Xuejiao(College of Hou Bo,Xinjiang Medical University,Karamay Xinjiang 834000,China)

机构地区：[1]新疆医科大学厚博学院,新疆克拉玛依834000

出　　处：《西华师范大学学报（自然科学版）》2021年第3期268-272,共5页Journal of China West Normal University(Natural Sciences)

基　　金：新疆克拉玛依市创新人才工程项目(2017RC001A-187)。

摘　　要：为了更好地度量网络的容错性,运用数学归纳法和反证法,讨论了条件故障下k-元n-立方体的强Menger边连通度问题。证明了当k≥4,n≥2时,k-元n-立方体是(6n-8)-条件边故障容错强Menger边连通的;当k=3,n≥2时,3-元n-立方体是(4n-6)-条件边故障容错强Menger边连通的。最后举了一个反例证明该结论是最优的。通过对这个问题的讨论和证明,可以补充Qiao等关于超立方体(2-元n-立方体)的条件容错强Menger边连通度的结果,同时进一步改进了翟登鑫对这个问题的研究结果。The problem of strong Menger edge connectivity of k-ary n-cubes under conditional faults is discussed by mathematical induction and proof by contradiction for better measuring the fault tolerance of networks.It is proved that k-ary n-cube is(6n-8)-conditional edge-fault-tolerance strongly Menger edge connected when k≥4,n≥2 and 3-ary n-cube is(4n-6)-conditional edge-fault-tolerance strongly Menger edge connected when k=3,n≥2.Finally, a counter example is given to prove that the conclusion is optimal.These discussions and proving have supplemented the results of Qiao et al.on the conditional fault-tolerance strong Menger edge connectivity of hypercubes(2-ary n-cubes) and improved the research results of Zhai Dengxin as well.

关 键 词：k-元n-立方体 容错性 强Menger边连通度 条件故障 边不交的路 

分 类 号：O157.5[理学—数学]