{"paper":{"title":"On groups all of whose Haar graphs are Cayley graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.CO","authors_text":"Da-Wei Yang, Istvan Kovacs, Yan-Quan Feng","submitted_at":"2017-07-11T00:45:04Z","abstract_excerpt":"A Cayley graph of a group $H$ is a finite simple graph $\\Gamma$ such that ${\\rm Aut}(\\Gamma)$ contains a subgroup isomorphic to $H$ acting regularly on $V(\\Gamma)$, while a Haar graph of $H$ is a finite simple bipartite graph $\\Sigma$ such that ${\\rm Aut}(\\Sigma)$ contains a subgroup isomorphic to $H$ acting semiregularly on $V(\\Sigma)$ and the $H$-orbits are equal to the bipartite sets of $\\Sigma$. A Cayley graph is a Haar graph exactly when it is bipartite, but no simple condition is known for a Haar graph to be a Cayley graph. In this paper, we show that the groups $D_6, \\, D_8, \\, D_{10}$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1707.03090","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"}