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The intersection graph of ideals of $R$, denoted by $G(R)$, is a graph with the vertex set $I(R)^*$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I\\cap J\\neq 0$. In this paper, it is shown that $G(\\mathbb{Z}_n)$, for every positive integer $n$, is a weakly perfect graph. Also, for some values of $n$, we give an explicit formula for the vertex chromatic number of $G(\\mathbb{Z}_n)$. Furthermore, it i"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1305.6287","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/publicdomain/","primary_cat":"math.AC","submitted_at":"2013-05-27T18:29:12Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"5b1563f97c4596518a763799478a4570648de2cb8e085da43b89cfead059f939","abstract_canon_sha256":"c53f604b0fc2dda705c8c2b47b5cef0dfc634681c99dbe90e8a9ecbcb4c42ace"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:24:51.666513Z","signature_b64":"nqMQ4uUT8X7S07QzTPlOfEBKlgKs6JJu92TwNslAPqFFpAoqQahYEz2B3QeMC7pGnZNcz0eE1NVax5w3NUHTBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f095d921da2ee5183275b2b941c05397995b7bd98df81a564324a434935f86fa","last_reissued_at":"2026-05-18T03:24:51.665941Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:24:51.665941Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The intersection graph of ideals of $\\mathbb{Z}_n$ is\\\\ weakly perfect","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"M.J. Nikmehr, R.Nikandish","submitted_at":"2013-05-27T18:29:12Z","abstract_excerpt":"A graph is called weakly perfect if its vertex chromatic number equals its clique number. Let $R$ be a ring and $I(R)^*$ be the set of all left proper non-trivial ideals of $R$. The intersection graph of ideals of $R$, denoted by $G(R)$, is a graph with the vertex set $I(R)^*$ and two distinct vertices $I$ and $J$ are adjacent if and only if $I\\cap J\\neq 0$. In this paper, it is shown that $G(\\mathbb{Z}_n)$, for every positive integer $n$, is a weakly perfect graph. Also, for some values of $n$, we give an explicit formula for the vertex chromatic number of $G(\\mathbb{Z}_n)$. 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