{"paper":{"title":"Cayley properties of the line graphs induced by consecutive layers of the hypercube","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"S.Morteza Mirafzal","submitted_at":"2017-11-07T19:51:56Z","abstract_excerpt":"Let $n >3$ and $ 0< k < \\frac{n}{2} $ be integers. In this paper, we investigate some algebraic properties of the line graph of the graph $ {Q_n}(k,k+1) $ where $ {Q_n}(k,k+1) $ is the subgraph of the hypercube $Q_n$ which is induced by the set of vertices of weights $k$ and $k+1$. In the first step, we determine the automorphism groups of these graphs for all values of $n,k$. In the second step, we study Cayley properties of the line graphs of these graphs. In particular, we show that if $k\\geq 3$ and $ n \\neq 2k+1$, then except for the cases $k=3, n=9$ and $k=3, n=33$, the line graph of the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.02701","kind":"arxiv","version":4},"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"}