50 research outputs found

    Fault diagnosability of regular graphs

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    An interconnection network\u27s diagnosability is an important measure of its self-diagnostic capability. In 2012, Peng et al. proposed a measure for fault diagnosis of the network, namely, the hh-good-neighbor conditional diagnosability, which requires that every fault-free node has at least hh fault-free neighbors. There are two well-known diagnostic models, PMC model and MM* model. The {\it hh-good-neighbor diagnosability} under the PMC (resp. MM*) model of a graph GG, denoted by thPMC(G)t_h^{PMC}(G) (resp. thMMβˆ—(G)t_h^{MM^*}(G)), is the maximum value of tt such that GG is hh-good-neighbor tt-diagnosable under the PMC (resp. MM*) model. In this paper, we study the 22-good-neighbor diagnosability of some general kk-regular kk-connected graphs GG under the PMC model and the MM* model. The main result t2PMC(G)=t2MMβˆ—(G)=g(kβˆ’1)βˆ’1t_2^{PMC}(G)=t_2^{MM^*}(G)=g(k-1)-1 with some acceptable conditions is obtained, where gg is the girth of GG. Furthermore, the following new results under the two models are obtained: t2PMC(HSn)=t2MMβˆ—(HSn)=4nβˆ’5t_2^{PMC}(HS_n)=t_2^{MM^*}(HS_n)=4n-5 for the hierarchical star network HSnHS_n, t2PMC(Sn2)=t2MMβˆ—(Sn2)=6nβˆ’13t_2^{PMC}(S_n^2)=t_2^{MM^*}(S_n^2)=6n-13 for the split-star networks Sn2S_n^2 and t2PMC(Ξ“n(Ξ”))=t2MMβˆ—(Ξ“n(Ξ”))=6nβˆ’16t_2^{PMC}(\Gamma_{n}(\Delta))=t_2^{MM^*}(\Gamma_{n}(\Delta))=6n-16 for the Cayley graph generated by the 22-tree Ξ“n(Ξ”)\Gamma_{n}(\Delta)

    A Local Diagnosis Algorithm for Hypercube-like Networks under the BGM Diagnosis Model

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    System diagnosis is process of identifying faulty nodes in a system. An efficient diagnosis is crucial for a multiprocessor system. The BGM diagnosis model is a modification of the PMC diagnosis model, which is a test-based diagnosis. In this paper, we present a specific structure and propose an algorithm for diagnosing a node in a system under the BGM model. We also give a polynomial-time algorithm that a node in a hypercube-like network can be diagnosed correctly in three test rounds under the BGM diagnosis model
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