{"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. Moreover we determine the supremum of the smallest eigenval"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1105.5490","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"}