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The proper reduced power graph $\\mathcal{RP}^*(G)$ of $G$ is the subgraph of $\\mathcal{RP}(G)$ induced on $G\\setminus \\{e\\}$. In this paper, we classify the finite groups whose reduced power graph (resp. proper reduced power graph) is one of complete $k$-partite, acyclic, triangle free or claw-free (resp. comple"},"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":"1804.00728","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-02T20:55:42Z","cross_cats_sorted":[],"title_canon_sha256":"207b7475c4c1a8b6718f06baf0f38af26843caa3a500ebb81f948cbf62f6ca80","abstract_canon_sha256":"1718e163917f44ba470e1caa59e28240f811870983b4f5690c75947a5b05735a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:24.577604Z","signature_b64":"K1dN0J+uHq5t9qagLQQwatCexWGNc1DpqECWn4cKyxkMO+PNki4WaGRQBxOUfaiyNCMcmX1LYbkg9tQssD+UBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"11655431fcda9449d9d92e2ba3e5d03fd461ca9fa69e1afb7355226d93371789","last_reissued_at":"2026-05-18T00:03:24.577127Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:24.577127Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some results on the reduced power graph of a group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"R. 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