{"paper":{"title":"On graphs with $m(\\partial^L_1)=n-3$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lu Lu, Qiongxiang Huang, Xueyi Huang","submitted_at":"2017-04-11T02:36:07Z","abstract_excerpt":"Let $\\partial^L_1\\ge\\partial^L_2\\ge\\cdots\\ge\\partial^L_n$ be the distance Laplacian eigenvalues of a connected graph $G$ and $m(\\partial^L_i)$ the multiplicity of $\\partial^L_i$. It is well known that the graphs with $m(\\partial^L_1)=n-1$ are complete graphs. Recently, the graphs with $m(\\partial^L_1)=n-2$ have been characterized by Celso et al. In this paper, we completely determine the graphs with $m(\\partial^L_1)=n-3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03122","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"}