A Short Note on the 1; 2-Good-Neighbor Diagnosability of Balanced Hypercubes
A Short Note on the 1; 2-Good-Neighbor Diagnosability of Balanced Hypercubes
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关于 1 的简短说明；
DOI：
10.1142/s0219265916500018
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发表时间：
2016
影响因子：
0.7
通讯作者：
Dongxue Yang
中科院分区：
文献类型：
--
作者：
Meimei Gu;Rongxia Hao;Dongxue Yang
让tc(G)和tg(G)分别是图G的条件可诊断性和g-好邻居可诊断性。与一般条件可诊断性的概念相比，g-好邻居条件可诊断性的概念限制较少。特别地，条件故障集概念要求任何顶点，无论故障与否，都至少有一个非故障邻居；而1-好邻居故障只要求一个非故障顶点至少有一个非故障邻居。与条件可诊断性相比，g-好邻居可诊断性很有趣，因为它具有更强的容忍能力。在本文中，我们研究了平衡超立方体BHn t1(BHn) 和tc(BHn) 之间的等式关系。即针对PMC模型下和针对MM模型下；进一步，得到PMC模型和MM模型下n ≥ 2时的2-好邻居诊断性t2(BHn)=4n−1。
Lettc(G)andtg(G)bethe conditional diagnosabilityandg-good-neighbor diagnosability, respectively, of a graphG. The notion of theg-good-neighbor conditional diagnosability is less restrictive as compared with that of the conditional diagnosability in general. Particularly, the conditional faulty set notion requires that, any vertex, faulty or not, have at least one non-faulty neighbor; while the 1-good-neighbor faulty only requires that a non-faulty vertex have at least one non-faulty neighbor. Compared with conditional diagnosability,g-good-neighbor diagnosability is interesting since it characterizes a stronger tolerance capability. In this paper, we investigate the equal relation betweent1(BHn) andtc(BHn) for the balanced hypercubesBHn. That isforunder the PMC model andforunder the MM model; Furthermore, the 2-good-neighbor diagnosabilityt2(BHn) = 4n− 1 for n ≥ 2 under the PMC model and the MM model is obtained.