{"paper":{"title":"On Lichnerowicz sharp distance-regular graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Heng Zhang, Kaizhe Chen, Shiping Liu","submitted_at":"2026-02-11T00:53:14Z","abstract_excerpt":"The first non-zero Laplacian eigenvalue $\\lambda_1$ of a finite graph is bounded below by its minimum Lin--Lu--Yau curvature $\\kappa$. This is a discrete analogue of the classical Lichnerowicz Theorem. A graph with $\\lambda_1=\\kappa$ is called Lichnerowicz sharp. In this note, we give a new proof of the classification of Lichnerowicz sharp distance-regular graphs, which was first obtained by M\\\"unch and strengthens the corresponding classification by Cushing, Kamtue, Koolen, Liu, M\\\"unch, and Peyerimhoff, which required an extra spectral condition. As a key preparatory step, we provide a class"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2602.10396","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2602.10396/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}