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Abstract

An interconnection network's 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 h-good-neighbor conditional diagnosability, which requires that every fault-free node has at least h fault-free neighbors. There are two well-known diagnostic models, PMC model and MM* model. The h-good-neighbor diagnosability under the PMC (resp. MM*) model of a graph G, denoted by thPMC(G) (resp. thMM*(G)), is the maximum value of t such that G is h-good-neighbor t-diagnosable under the PMC (resp. MM*) model. In this paper, we study the 2-good-neighbor diagnosability of some general k-regular k-connected graphs G under the PMC model and the MM* model. The main result t2PMC(G)=t2MM*}(G)=g(k-1)-1 with some acceptable conditions is obtained, where g is the girth of G. Furthermore, the following new results under the two models are obtained: t2PMC(HSn)=t2MM*}(HSn)=4n-5 for the hierarchical star network HSn, t2PMC(Sn2)=t2MM*(Sn2)=6n-13 for the split-star networks Sn2 and t2PMC}(Γn(Δ))=t2MM*}(Γn(Δ))=6n-16 for the Cayley graph generated by the 2-tree Γn(Δ).

Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.

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