{"paper":{"title":"Proof of a conjecture of Abdollahi-Akbari-Maimani concerning the non-commutative graph of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Armando S\\'anchez-Nungaray, Daniel G. Mendoza, Luis A. Dupont","submitted_at":"2017-06-22T00:12:51Z","abstract_excerpt":"The non--commuting graph $\\Gamma(G)$ of a non--abelian group $G$ is defined as follows. The vertex set $V(\\Gamma(G))$ of $\\Gamma(G)$ is $G\\setminus Z(G)$ where $Z(G)$ denotes the center of $G$ and two vertices $x$ and $y$ are adjacent if and only if $xy\\neq yx$. For non--abelian finite groups $G$ and $H$ it is conjectured that if $\\Gamma(G) \\cong \\Gamma(H)$, then $|G|=|H|$. We prove the conjecture."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.07142","kind":"arxiv","version":2},"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"}