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In the present paper, we show that if the Kneser graph $K(n,k)$ is of even order where $n$ is an odd integer or both of the integers $n,k $ are even, then $K(n,k)$ is a vertex-transitive non Cayley graph. Although, these are special cases of Godsil [8], unlike his proof that uses some very deep group-theoretical facts, ours uses no heavy group-theoretic facts."},"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":"1702.02095","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2017-02-07T16:52:10Z","cross_cats_sorted":[],"title_canon_sha256":"4ac5d7a0f719b6758b4a021a98cade026524be4a7273fc02cc505770448707ab","abstract_canon_sha256":"0ed74cf082b18211d8fef5fdf6bffadb151b2d62ab707a84ec284377ce534070"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:13.842830Z","signature_b64":"mgHAV3dKOydN1QWWBOv+u6GmtVrT3ZnnUvGzeQRH1ocIE7NVVt5TmtTOWmvJEiyUwNkvAqo3RP0cWzQ90mUrDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"efcff9c5576037ce7513dcba874586d5da0efdf6b98fc4dcebe11e76deb95683","last_reissued_at":"2026-05-18T00:35:13.842373Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:13.842373Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"More odd graph theory from another point of view","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"S. 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