{"paper":{"title":"Full characterization of graphs having certain normalized Laplacian eigenvalue of multiplicity $n-3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Fenglei Tian, Yiju Wang","submitted_at":"2020-12-22T11:03:14Z","abstract_excerpt":"Let $G$ be a connected simple graph of order $n$. Let $\\rho_1(G)\\geq \\rho_2(G)\\geq \\cdots \\geq \\rho_{n-1}(G)> \\rho_n(G)=0$ be the eigenvalues of the normalized Laplacian matrix $\\mathcal{L}(G)$ of $G$. Denote by $m(\\rho_i)$ the multiplicity of the normalized Laplacian eigenvalue $\\rho_i$. Let $\\nu(G)$ be the independence number of $G$. In this paper, we give a full characterization of graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$, which answers a remaining problem in [S. Sun, K.C. Das, On the multiplicities of normalized Laplacian eigenvalues of graphs, Linear Algebra "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2012.11929","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2012.11929/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"}