{"paper":{"title":"Non-bipartite distance-regular graphs with a small smallest eigenvalue","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack Koolen, Yifan Jing, Zhi Qiao","submitted_at":"2019-01-03T06:45:43Z","abstract_excerpt":"In 2017, Qiao and Koolen showed that for any fixed integer $D\\geq 3$, there are only finitely many such graphs with $\\theta_{\\min}\\leq -\\alpha k$, where $0<\\alpha<1$ is any fixed number. In this paper, we will study non-bipartite distance-regular graphs with relatively small $\\theta_{\\min}$ compared with $k$. In particular, we will show that if $\\theta_{\\min}$ is relatively close to $-k$, then the odd girth $g$ must be large. Also we will classify the non-bipartite distance-regular graphs with $\\theta_{\\min} \\leq \\frac{D-1}{D}$ for $D =4,5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.01157","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"}