扩展k元n立方体的1-好邻诊断度

The 1-Good-Neighbor Diagnosability of Augmented k-Ary n-Cubes

摘要: 现如今，一个多重处理器系统的诊断度是一个非常重要的研究课题，它是度量多重处理器系统故障诊断能力的重要参数。2012年，Peng等人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维扩展k元n立方体是超立方体的一个重要变形。在本文中，我们证明了扩展k元n立方体在PMC模型下和MM*模型下的1-好邻诊断度是8n-9(n≥4,k≥4)。

Abstract: Nowadays, diagnosability is an important research topic and parameter in measuring the fault di-agnosis of multiprocessor systems. In 2012, Peng et al. proposed a new measure for fault diagnosis of the system, which was called g-good-neighbor diagnosability that restrained every fault-free node containing at least g fault-free neighbors. The n-dimensional augmented k-ary n-cube is an important variant of the hypercube. In this paper, we prove that the 1-good-neighbor diagnosibility of augmented k-aryn-cube under the PMC model and the MM* model is 8n-9 forn≥4,k≥4.