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In this paper, we show that $H(n, k)$ is an arc-transitive graph. Also, we show that $H(n,1)$ is a distance-transitive Cayley graph. Finally, we determine the automorphism group of the graph $H(n, 1)$ and show that $Aut(H(n, 1)) \\cong Sym([n] )$ $\\times \\mathbb{Z}_2$, where $\\mathbb{Z}_2$ is the cyclic 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":"1804.04570","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GR","submitted_at":"2018-04-12T15:32:22Z","cross_cats_sorted":[],"title_canon_sha256":"93c817c04597a46ff89bfc23f73e4dede626dd7caee80d6a97497a57a82cbfec","abstract_canon_sha256":"aa99a2549fe6eb0226607b628d04cdea28470fb92c4b12c3d196307de1b742d8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:18:36.944655Z","signature_b64":"DxbohrEAiV3gnoTt0doX0IhY3yk4AAEzYoNu+3y9nyD9/IWfOi+zX12IFQI+WbZ8xA2py80TlgND1Fgn+om7DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e89555108294537aaa94f7d635bd70f1886e536b93504f7092093e91d55b67d6","last_reissued_at":"2026-05-18T00:18:36.944043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:18:36.944043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some algebraic properties of bipartite Kneser graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Ali Zafari, S. 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