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From these results, we determine the largest and second largest limit points of smallest eigenvalues of regular graphs less than -2. Moreover we determine the supremum of the smallest eigenval"},"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":"1105.5490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-05-27T07:40:57Z","cross_cats_sorted":[],"title_canon_sha256":"7f946925da415b971b99470ee4ccfe13c69ca45ec2ef4b96b64fdc9973b74c72","abstract_canon_sha256":"4c8616bebf1aba1d4b2d0361ae1d0900141aa0f1718459d91643c6d94d41244f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:21:11.567914Z","signature_b64":"tdjbRUjCnkqS4/HYWevm1tu83ll5Djh512OqaUIth2jRTo8XVfbcv9uoVvBgM6Z4TvX5uRgR5m2ohorsivxeAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3540ab5cbedb7fbd356bb1d422156d74890dfa4ac3252ceb6ef389e301d2fc49","last_reissued_at":"2026-05-18T04:21:11.567385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:21:11.567385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the limit points of the smallest eigenvalues of regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hyonju Yu","submitted_at":"2011-05-27T07:40:57Z","abstract_excerpt":"In this paper, we give infinitely many examples of (non-isomorphic) connected $k$-regular graphs with smallest eigenvalue in half open interval $[-1-\\sqrt2, -2)$ and also infinitely many examples of (non-isomorphic) connected $k$-regular graphs with smallest eigenvalue in half open interval $[\\alpha_1, -1-\\sqrt2)$ where $\\alpha_1$ is the smallest root$(\\approx -2.4812)$ of the polynomial $x^3+2x^2-2x-2$. From these results, we determine the largest and second largest limit points of smallest eigenvalues of regular graphs less than -2. 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