交叉立方体的1好邻连通度和诊断度  

The 1-Good-Neighbor Connectivity and Diagnosability of Crossed Cubes

作　　者：马晓蕾 王世英[1,2] 王贞化[1] 

机构地区：[1]河南师范大学,数学与信息科学学院,河南新乡 [2]河南师范大学,河南省大数据统计分析与优化控制工程实验室,河南新乡

出　　处：《应用数学进展》2016年第2期282-290,共9页Advances in Applied Mathematics

基　　金：国家自然科学基金资助项目(61370001);教育部博士点基金(博导类)资助项目(20111401110005)。

摘　　要：连通度和诊断度是度量多处理器系统故障诊断能力的重要参数。2012年,Peng等提出了一个新的系统故障诊断方法,称为g好邻诊断度,它限制每个非故障顶点至少有g个非故障邻点。n维交叉立方体是超立方体的一个重要变形。本文证明了交叉立方体的1好邻连通度是2n – 2 (n ≥ 4),又证明了交叉立方体在PMC模型下的1好邻诊断度是2n – 1 (n ≥ 4)和在MM*模型下的1好邻诊断度是2n – 1 (n ≥ 5)。Connectivity and diagnosability are important parameters in measuring the fault diagnosis of multiprocessor systems. In 2012, Peng et al. proposed a new measure for fault diagnosis of the system, which is called g-good-neighbor diagnosability that restrains every fault-free node con-taining at least g fault-free neighbors. The n-dimensional crossed cube is an important variant of the hypercube. In this paper, we prove that the 1-good-neighbor connectivity of crossed cube is 2n ? 2 for n ≥ 4, and the 1-good-neighbor diagnosability of crossed cube is 2n ? 1 under the PMC model for n ≥ 4 and the MM* model for n ≥ 5.

关 键 词：互连网络 图 诊断度 交叉立方体 

分 类 号：O1[理学—数学]