{"paper":{"title":"On generalized 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":"Dhiren Kumar Basnet, Jutirekha Dutta, Rajat Kanti Nath","submitted_at":"2016-04-13T06:49:00Z","abstract_excerpt":"Let $S, K$ be two subrings of a finite ring $R$. Then the generalized non-commuting graph of subrings $S, K$ of $R$, denoted by $\\Gamma_{S, K}$, is a simple graph whose vertex set is $(S \\cup K) \\setminus (C_K(S) \\cup C_S(K))$ and two distinct vertices $a, b$ are adjacent if and only if $a \\in S$ or $b \\in S$ and $ab \\neq ba$. We determine the diameter, girth and some dominating sets for $\\Gamma_{S, K}$. Some connections between the $\\Gamma_{S, K}$ and $\\Pr(S, K)$ are also obtained. Further, $\\Z$-isoclinism between two pairs of finite rings is defined and showed that the generalized non-commut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.03671","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"}