有缺失边的n维增强超立方体在MM^*模型下的局部可诊断性  

Local Diagnosability of n-Dimensional Enhanced Hypercubes with Missing Edges under the MM* Model

作　　者：王世英 张雪芳 赵丽娜 

机构地区：[1]山西师范大学,数学与计算机科学学院,山西 太原

出　　处：《应用数学进展》2022年第2期726-738,共13页Advances in Applied Mathematics

摘　　要：多重处理器系统的诊断性在互联网的可靠性中扮演着重要的角色。n维增强超立方体Qn,k是由n维超立方体Qn添加一些互补边得到的。n维增强超立方体Qn,k有许多好的性质。这篇文章中,我们首先证明了在MM*模型下Qn,k具有强局部诊断性,然后证明了在MM*模型下Qn,k即使存在n-1条缺失边时仍具有强局部诊断性,并且证明了缺失边的数目n-1是最优值。The diagnosability of multiprocessor systems plays an important role in the reliability of the Internet. The n-dimensional enhanced hypercube Qn,k is obtained by adding some complementary edges to n-dimensional hypercubes. The n-dimensional enhanced hypercube Qn,k has many good properties. In this paper, we prove Qn,k has the strong local diagnosability property under the MM* model. Then we prove that Qn,k(n≤6) keeps the strong local diagnosability property even if there exist n-1 missing edges in it under the MM* model and the result is optimal with respect to the number of missing edges.

关 键 词：互连网络 强局部诊断度 n维增强超立方体 延展星结构 MM^*模型 

分 类 号：O157.5[理学—数学]