{"paper":{"title":"Automorphism groups of Cayley graphs generated by block transpositions and regular Cayley maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Annachiara Korchmaros, Istv\\'an Kov\\'acs","submitted_at":"2015-11-23T15:21:44Z","abstract_excerpt":"This paper deals with the Cayley graph $\\mathrm{Cay}(\\mathrm{Sym}_n,T_n),$ where the generating set consists of all block transpositions. A motivation for the study of these particular Cayley graphs comes from current research in Bioinformatics. As the main result, we prove that Aut$(\\mathrm{Cay}(\\mathrm{Sym}_n,T_n))$ is the product of the left translation group by a dihedral group $\\mathsf{D}_{n+1}$ of order $2(n+1)$. The proof uses several properties of the subgraph $\\Gamma$ of $\\mathrm{Cay}(\\mathrm{Sym}_n,T_n)$ induced by the set $T_n$. In particular, $\\Gamma$ is a $2(n-2)$-regular graph wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07268","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"}