{"paper":{"title":"Light tails and the Hermitian dual polar graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jack Koolen, Zhi Qiao","submitted_at":"2015-11-17T01:09:34Z","abstract_excerpt":"Juri\\'{s}i\\v{c} et al. conjectured that if a distance-regular graph $\\Gamma$ with diameter $D$ at least three has a light tail, then one of the following holds:\n  1.$a_1 =0$;\n  2.$\\Gamma$ is an antipodal cover of diameter three;\n  3.$\\Gamma$ is tight;\n  4.$\\Gamma$ is the halved $2D+1$-cube;\n  5.$\\Gamma$ is a Hermitian dual polar graph $^2A_{2D-1}(r)$ where $r$ is a prime power.\n  In this note, we will consider the case when the light tail corresponds to the eigenvalue $-\\frac{k}{a_1 +1}$. Our main result is:\n  Theorem Let $\\Gamma$ be a non-bipartite distance-regular graph with valency $k \\geq "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.05239","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"}