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 , 王贞化 :河南师范大学,数学与信息科学学院,河南 新乡; 王世英 :河南师范大学,数学与信息科学学院,河南 新乡;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;

关键词: 互连网络诊断度交叉立方体Interconnection Network Graph Diagnosability Crossed Cube

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)。

Abstract: 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.

文章引用: 马晓蕾 , 王世英 , 王贞化 (2016) 交叉立方体的1好邻连通度和诊断度。 应用数学进展, 5, 282-290. doi: 10.12677/AAM.2016.52036

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