{"paper":{"title":"Graph Automorphisms from the Geometric Viewpoint","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Wen-Xue Du, Yi-Zheng Fan","submitted_at":"2013-12-10T12:25:43Z","abstract_excerpt":"An automorphism of a graph $G=(V,E)$ is a bijective map $\\phi$ from $V$ to itself such that $\\phi(v_i)\\phi(v_j)\\in E$ $\\Leftrightarrow$ $v_i v_j\\in E$ for any two vertices $v_i$ and $v_j$. Denote by $\\mathfrak{G}$ the group consisting of all automorphisms of $G$. Apparently, an automorphism of $G$ can be regarded as a permutation on $[n]=\\{1,\\ldots,n\\}$, provided that $G$ has $n$ vertices. For each permutation $\\sigma$ on $[n]$, there is a natural action on any given vector $\\boldsymbol{u}=(u_1,\\ldots,u_n)^t\\in \\mathbb{C}^n$ such that $\\sigma\\boldsymbol{u}=(u_{\\sigma^{-1}1},u_{\\sigma^{-1}2},\\l"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.2778","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"}