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- W2953014796 abstract "Extra connectivity and the pessimistic diagnosis are two crucial subjects for a multiprocessor system's ability to tolerate and diagnose faulty processor. The pessimistic diagnosis strategy is a classic strategy based on the PMC model in which isolates all faulty vertices within a set containing at most one fault-free vertex. In this paper, the result that the pessimistic diagnosability $t_p(G)$ equals the extra connectivity $kappa_{1}(G)$ of a regular graph $G$ under some conditions are shown. Furthermore, the following new results are gotten: the pessimistic diagnosability $t_p(S_n^2)=4n-9$ for split-star networks $S_n^2$, $t_p(Gamma_n)=2n-4$ for Cayley graphs generated by transposition trees $Gamma_n$, $t_p(Gamma_{n}(Delta))=4n-11$ for Cayley graph generated by the $2$-tree $Gamma_{n}(Delta)$, $t_{p}(BP_n)=2n-2$ for the burnt pancake networks $BP_n$. As corollaries, the known results about the extra connectivity and the pessimistic diagnosability of many famous networks including the alternating group graphs, the alternating group networks, BC networks, the $k$-ary $n$-cube networks etc. are obtained directly." @default.
- W2953014796 created "2019-06-27" @default.
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- W2953014796 date "2017-01-29" @default.
- W2953014796 modified "2023-09-24" @default.
- W2953014796 title "Equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs" @default.
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- W2953014796 doi "https://doi.org/10.48550/arxiv.1701.08355" @default.
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