{"paper":{"title":"Some Properties of the Nil-Graphs of Ideals of Commutative Rings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"F. Shaveisi, R. Nikandish","submitted_at":"2016-11-10T08:24:25Z","abstract_excerpt":"Let $R$ be a commutative ring with identity and ${\\rm Nil}(R)$ be the set of nilpotent elements of $R$. The nil-graph of ideals of $R$ is defined as the graph $\\mathbb{AG}_N(R)$ whose vertex set is $\\{I:\\ (0)\\neq I\\lhd R$ and there exists a non-trivial ideal $J$ such that $IJ\\subseteq {\\rm Nil}(R)\\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ\\subseteq {\\rm Nil}(R)$. Here, we study conditions under which $\\mathbb{AG}_N(R)$ is complete or bipartite. Also, the independence number of $\\mathbb{AG}_N(R)$ is determined, where $R$ is a reduced ring. Finally, we classify Arti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03730","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"}