{"paper":{"title":"On non-commuting graph of a finite ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RA","authors_text":"D. K. Basnet, J. Dutta","submitted_at":"2017-03-15T09:28:19Z","abstract_excerpt":"The non-commuting graph $\\Gamma_R$ of a finite ring $R$ with center $Z(R)$ is a simple undirected graph whose vertex set is $R \\setminus Z(R)$ and two distinct vertices $a$ and $b$ are adjacent if and only if $ab \\ne ba$. In this paper, we show that $\\Gamma_R$ is not isomorphic to certain graphs of any finite non-commutative ring $R$. Some connections between $\\Gamma_R$ and commuting probability of $R$ are also obtained. Further, it is shown that the non-commuting graphs of two $\\mathbb{Z}$-isoclinic rings are isomorphic if the centers of the rings have same order"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05039","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"}