{"paper":{"title":"On $g$-good-neighbor conditional diagnosability of $(n, k)$-star networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Min Xu, Yulong Wei","submitted_at":"2017-03-22T10:52:46Z","abstract_excerpt":"The $g$-good-neighbor conditional diagnosability is a new measure for fault diagnosis of systems. Xu et al. [Theor. Comput. Sci. 659 (2017) 53--63] determined the $g$-good-neighbor conditional diagnosability of $(n, k)$-star networks $S_{n, k}$ (i.e., $t_g(S_{n, k})$) with $1\\leq k\\leq n-1$ for $1\\leq g\\leq n-k$ under the PMC model and the MM$^*$ model. In this paper, we determine $t_g(S_{n, k})$ for all the remaining cases with $1\\leq k\\leq n-1$ for $1\\leq g\\leq n-1$ under the two models, from which we can obtain the $g$-good-neighbor conditional diagnosability of the star graph obtained by L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.07599","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}