{"paper":{"title":"On finite groups all of whose cubic Cayley graphs are integral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.GR","authors_text":"Kaishun Wang, Xuanlong Ma","submitted_at":"2014-09-17T10:41:15Z","abstract_excerpt":"For any positive integer $k$, let $\\mathcal{G}_k$ denote the set of finite groups $G$ such that all Cayley graphs ${\\rm Cay}(G,S)$ are integral whenever $|S|\\le k$. Est${\\rm \\acute{e}}$lyi and Kov${\\rm \\acute{a}}$cs \\cite{EK14} classified $\\mathcal{G}_k$ for each $k\\ge 4$. In this paper, we characterize the finite groups each of whose cubic Cayley graphs is integral. Moreover, the class $\\mathcal{G}_3$ is characterized. As an application, the classification of $\\mathcal{G}_k$ is obtained again, where $k\\ge 4$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4939","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"}