{"paper":{"title":"Structure of the automorphism group of the augmented cube graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Ashwin Ganesan","submitted_at":"2015-08-27T17:03:40Z","abstract_excerpt":"\\noindent The augmented cube graph $AQ_n$ is the Cayley graph of $\\mathbb{Z}_2^n$ with respect to the set of $2n-1$ generators $\\{e_1,e_2, \\ldots,e_n, 00\\ldots0011, 00\\ldots0111, 11\\ldots1111 \\}$. It is known that the order of the automorphism group of the graph $AQ_n$ is $2^{n+3}$, for all $n \\ge 4$. In the present paper, we obtain the structure of the automorphism group of $AQ_n$ to be \\[ \\Aut(AQ_n) \\cong \\mathbb{Z}_2^n \\rtimes D_8~~(n \\ge 4),\\] where $D_8$ is the dihedral group of order 8. It is shown that the Cayley graph $AQ_3$ is non-normal and that $AQ_n$ is normal for all $n \\ge 4$. We"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07257","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"}