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In this paper, we classify the finite groups whose intersection graph of cyclic subgroups is one of totally disconnected, complete, star, path, cycle. We show that for a given finite group $G$, $girth(\\mathscr I_c (G)) \\in \\{3, \\infty\\}$. Moreover, we classify all finite non-cyclic abelian groups whose intersection"},"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":"1509.04574","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2015-09-15T14:17:33Z","cross_cats_sorted":[],"title_canon_sha256":"894f6328316739f15e3f6701cde9626c8e77fd183bcfe5e0c7c219da9ef038f4","abstract_canon_sha256":"3019cdc39c59ca61aa5655b93602e5ed77e3b4dc71732fc289f200faea944f00"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:58.537265Z","signature_b64":"5uCTm6/HlLXoa6mQ53QVRIj2ZBRQwuXW9Fd9B7X2oiivRTcycUCPpO8r/bfEKBo5CywR/pR6TgeLDx0Ls1MpAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1a30a8dedfad65493c404ec7cd2d3756a522e0921d5c45a41d0b0896b4908ff0","last_reissued_at":"2026-05-18T01:32:58.536629Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:58.536629Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Intersection graph of cyclic subgroups of groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"P. 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