{"paper":{"title":"Graphs with at most three distance eigenvalues different from $-1$ and $-2$","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":"2017-08-26T14:42:14Z","abstract_excerpt":"Let $G$ be a connected graph on $n$ vertices, and let $D(G)$ be the distance matrix of $G$. Let $\\partial_1(G)\\ge\\partial_2(G)\\ge\\cdots\\ge\\partial_n(G)$ denote the eigenvalues of $D(G)$. In this paper, we characterize all connected graphs with $\\partial_{3}(G)\\leq -1$ and $\\partial_{n-1}(G)\\geq -2$. By the way, we determine all connected graphs with at most three distance eigenvalues different from $-1$ and $-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.07979","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"}