{"paper":{"title":"Automorphism Groups of the Pancake Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xiao-Dong Zhang, Yun-Ping Deng","submitted_at":"2012-01-02T11:05:32Z","abstract_excerpt":"It is well-known that the pancake graphs are widely used as models for interconnection networks \\cite{Akers}. In this paper, some properties of the pancake graphs are investigated. We first prove that the pancake graph, denoted by $P_n (n\\geq 4),$ is super-connected and hyper-connected. Further, we study the symmetry of $P_n$ and completely determine its full automorphism group,which shows that $P_n (n\\geq 5)$ is a graphical regular representation of $S_n.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.0452","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"}