{"paper":{"title":"Component edge connectivity of the folded hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Shuli Zhao, Weihua Yang","submitted_at":"2018-03-04T07:33:50Z","abstract_excerpt":"The $g$-component edge connectivity $c\\lambda_g(G)$ of a non-complete graph $G$ is the minimum number of edges whose deletion results in a graph with at least $g$ components. In this paper, we determine the component edge connectivity of the folded hypercube $c\\lambda_{g+1}(FQ_{n})=(n+1)g-(\\sum\\limits_{i=0}^{s}t_i2^{t_i-1}+\\sum\\limits_{i=0}^{s} i\\cdot 2^{t_i})$ for $g\\leq 2^{[\\frac{n+1}2]}$ and $n\\geq 5$, where $g$ be a positive integer and $g=\\sum\\limits_{i=0}^{s}2^{t_i}$ be the decomposition of $g$ such that $t_0=[\\log_{2}{g}],$ and $t_i=[\\log_2({g-\\sum\\limits_{r=0}^{i-1}2^{t_r}})]$ for $i\\g"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.01312","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"}