{"paper":{"title":"On fault tolerance of (n,k)-star networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun-Ming Xu, Xiang-jun Li, Yong-ni Guan, Zheng Yan","submitted_at":"2016-11-20T01:43:10Z","abstract_excerpt":"Fault tolerance of an $(n,k)$-star network is measured by its $h$-super connectivity $\\kappa_s^{(h)}$ or $h$-super edge-connectivity $\\lambda_s^{(h)}$. Li {\\it et al.} [Appl. Math. Comput. 248 (2014), 525-530; Math. Sci. Lett. 1 (2012), 133-138] determined $\\kappa_s^{(h)}$ and $\\lambda_s^{(h)}$ for $0\\leq h\\leq n-k$. This paper determines $\\kappa_s^{(h)}=\\lambda_s^{(h)}=\\frac{(h+1)!(n-h-1)}{(n-k)!}$ for $n-k\\leq h \\leq n-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06460","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"}