{"paper":{"title":"On the Automorphism Groups of Regular Hyper-Stars and Folded Hyper-Stars","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"S. Morteza Mirafzal","submitted_at":"2011-03-18T10:06:12Z","abstract_excerpt":"The hyper-star graph $HS(n,k)$ is defined as follows : its vertex-set is the set of $ {0,1} $-sequences of length $n$ with weight $k$, where the weight of a sequence $v$ is the number of $1^,s$ in $v$, and two vertices are adjacent if and only if one can be obtained from the other by exchanging the first symbol with a different symbol (1 with 0, or 0 with 1) in another position.\n  In this paper, we will find the automorphism groups of regular hyper-star and folded hyper-star graphs. Then, we will show that, only the graphs HS(4,2) and FHS(4,2) are Cayley graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3584","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"}