{"paper":{"title":"Quadratic unitary Cayley graphs of finite commutative rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Sanming Zhou, Xiaogang Liu","submitted_at":"2015-04-12T05:48:51Z","abstract_excerpt":"The purpose of this paper is to study spectral properties of a family of Cayley graphs on finite commutative rings. Let $R$ be such a ring and $R^\\times$ its set of units. Let $Q_R=\\{u^2: u\\in R^\\times\\}$ and $T_R=Q_R\\cup(-Q_R)$. We define the quadratic unitary Cayley graph of $R$, denoted by $\\mathcal{G}_R$, to be the Cayley graph on the additive group of $R$ with respect to $T_R$; that is, $\\mathcal{G}_R$ has vertex set $R$ such that $x, y \\in R$ are adjacent if and only if $x-y\\in T_R$. It is well known that any finite commutative ring $R$ can be decomposed as $R=R_1\\times R_2\\times\\cdots\\t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02934","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"}