{"paper":{"title":"Generalized Measures of Edge Fault Tolerance in (n,k)-star Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun-Ming Xu, Xiang-jun Li","submitted_at":"2012-04-03T02:17:44Z","abstract_excerpt":"This paper considers a kind of generalized measure $\\lambda_s^{(h)}$ of fault tolerance in the $(n,k)$-star graph $S_{n,k}$ for $2\\leqslant k \\leqslant n-1$ and $0\\leqslant h \\leqslant n-k$, and determines $\\lambda_s^{(h)}(S_{n,k})=\\min\\{(n-h-1)(h+1), (n-k+1)(k-1)\\}$, which implies that at least $\\min\\{(n-k+1)(k-1),(n-h-1)(h+1)\\}$ edges of $S_{n,k}$ have to remove to get a disconnected graph that contains no vertices of degree less than $h$. This result shows that the $(n,k)$-star graph is robust when it is used to model the topological structure of a large-scale parallel processing system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0573","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"}