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In particular, the rainbow connection number of $\\Gamma_G$ is $2$. Moreover, for any positive integer $k$, we prove that there exist infinitely many non-abelian groups $G$ such that the rainbow $k$-connectivity of $\\Gamma_G$ is $2$."},"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":"1506.04378","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-14T11:04:38Z","cross_cats_sorted":[],"title_canon_sha256":"47e8d896eedc59564127a8fec9fca9286ac0cd5535fb4495fa7596fc258843bc","abstract_canon_sha256":"369abbd75ee3dc8b87db9050c01e159cba74c822c6523d4c4f72dbf6e14b773e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:49:54.695210Z","signature_b64":"o0QKoWB35ootRzSUuezGaB7GJ1wQ79qvRKOrq+j4xvtNWtfhT4/ooAMQb+ed1bcV2/3ca/Rma1Qk3uyFmhc7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"246d8ca6a5aa621ab4293dd1f0da210f687fde8e000e893b839722aabc1a820f","last_reissued_at":"2026-05-18T01:49:54.694638Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:49:54.694638Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rainbow connectivity of the non-commuting graph of a finite group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kaishun Wang, Xuanlong Ma, Yulong Wei","submitted_at":"2015-06-14T11:04:38Z","abstract_excerpt":"Let $G$ be a finite non-abelian group. The non-commuting graph $\\Gamma_G$ of $G$ has the vertex set $G\\setminus Z(G)$ and two distinct vertices $x$ and $y$ are adjacent if $xy\\ne yx$, where $Z(G)$ is the center of $G$. We prove that the rainbow $2$-connectivity of $\\Gamma_G$ is $2$. In particular, the rainbow connection number of $\\Gamma_G$ is $2$. Moreover, for any positive integer $k$, we prove that there exist infinitely many non-abelian groups $G$ such that the rainbow $k$-connectivity of $\\Gamma_G$ is $2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.04378","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.04378","created_at":"2026-05-18T01:49:54.694715+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.04378v1","created_at":"2026-05-18T01:49:54.694715+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.04378","created_at":"2026-05-18T01:49:54.694715+00:00"},{"alias_kind":"pith_short_12","alias_value":"ERWYZJVFVJRB","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"ERWYZJVFVJRBVNBJ","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"ERWYZJVF","created_at":"2026-05-18T12:29:19.899920+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5","json":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5.json","graph_json":"https://pith.science/api/pith-number/ERWYZJVFVJRBVNBJHXI7BWRBB5/graph.json","events_json":"https://pith.science/api/pith-number/ERWYZJVFVJRBVNBJHXI7BWRBB5/events.json","paper":"https://pith.science/paper/ERWYZJVF"},"agent_actions":{"view_html":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5","download_json":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5.json","view_paper":"https://pith.science/paper/ERWYZJVF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.04378&json=true","fetch_graph":"https://pith.science/api/pith-number/ERWYZJVFVJRBVNBJHXI7BWRBB5/graph.json","fetch_events":"https://pith.science/api/pith-number/ERWYZJVFVJRBVNBJHXI7BWRBB5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5/action/storage_attestation","attest_author":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5/action/author_attestation","sign_citation":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5/action/citation_signature","submit_replication":"https://pith.science/pith/ERWYZJVFVJRBVNBJHXI7BWRBB5/action/replication_record"}},"created_at":"2026-05-18T01:49:54.694715+00:00","updated_at":"2026-05-18T01:49:54.694715+00:00"}