{"paper":{"title":"On the conjecture of vertex-transitivity of Dcell","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Huazhong L\\\"u","submitted_at":"2018-05-18T11:00:48Z","abstract_excerpt":"Gu et al. in [Inform. Process. Lett. 134 (2018) 52--56] conjectured that the data center network $D_{k,n}$ is vertex-transitive for all $k\\geq0$ and $n\\geq2$. In this paper, we show that $D_{k,n}$ is vertex-transitive for $k\\leq1$ and $n\\geq2$, and it is not vertex-transitive for all $k\\geq2$ and $n\\geq2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.07139","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"}