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In this article we classify all groups $G$ for which $\\mathcal{P}_s(G)$ is line graph and Caley graph. Spectrum and permanent of the Laplacian matrix of the strong power graph $\\mathcal{P}_s(G)$ are found for any finite group $G$."},"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":"1504.06095","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-04-23T09:15:11Z","cross_cats_sorted":[],"title_canon_sha256":"d3c6693a4d910cb23b10c368a233d7ba0266325255da71a41cc52583c7a983a6","abstract_canon_sha256":"3c7d3d0298db05919cbf90ebf2bf39d51aa304193887e5b8cf442f6617bf1ee1"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:36:43.196558Z","signature_b64":"bTOdvPRttV9r/ldc6WTLECsPJkli1iw2ans9gGEaQPbSNtStG7py0GRPt7YG5JfG50oYsRqC8PYvl1MlrrT4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a81b43a729cad6a8b8bcccf7073a1f6618afe89543d3389f328fa3ac47dcb0cb","last_reissued_at":"2026-05-18T01:36:43.195916Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:36:43.195916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On some characterizations of strong power graphs of finite groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. 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