{"paper":{"title":"On conditional fault tolerance of hierarchical cubic networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun-Ming Xu, Min Liu, Xiang-jun Li, Zheng Yan","submitted_at":"2017-09-06T22:08:31Z","abstract_excerpt":"This paper considers the conditional fault tolerance, $h$-super connectivity $\\kappa^{h}$ and $h$-super edge-connectivity $\\lambda^{h}$ of the hierarchical cubic network $HCN_n$, an attractive alternative network to the hypercube, and shows $\\kappa^h(HCN_n)=\\lambda^h(HCN_n)=2^h(n+1-h)$ for any $h$ with $0\\leq h\\leq n-1$. The results imply that at least $2^h(n+1-h)$ vertices or edges have to be removed from $HCN_n$ to make it disconnected with no vertices of degree less than $h$, and generalize some known results."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.02013","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"}