{"paper":{"title":"Fault-tolerant analysis of augmented cubes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jun-Ming Xu, Meijie Ma, Yaxing Song","submitted_at":"2012-04-19T05:13:05Z","abstract_excerpt":"The augmented cube $AQ_n$, proposed by Choudum and Sunitha [S. A. Choudum, V. Sunitha, Augmented cubes, Networks 40 (2) (2002) 71-84], is a $(2n-1)$-regular $(2n-1)$-connected graph $(n\\ge 4)$. This paper determines that the 2-extra connectivity of $AQ_n$ is $6n-17$ for $n\\geq 9$ and the 2-extra edge-connectivity is $6n-9$ for $n\\geq 4$. That is, for $n\\geq 9$ (respectively, $n\\geq 4$), at least $6n-17$ vertices (respectively, $6n-9$ edges) of $AQ_n$ have to be removed to get a disconnected graph that contains no isolated vertices and isolated edges. When the augmented cube is used to model th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.4251","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"}