{"paper":{"title":"A lower bound of the least signless Laplacian eigenvalue of a graph","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Guanglong Yu, Shu-Guang Guo, Yong-Gao Chen","submitted_at":"2013-11-13T12:03:02Z","abstract_excerpt":"Let $G$ be a simple connected graph on $n$ vertices and $m$ edges. In [Linear Algebra Appl. 435 (2011) 2570-2584], Lima et al. posed the following conjecture on the least eigenvalue $q_n(G)$ of the signless Laplacian of $G$: $\\displaystyle q_n(G)\\ge {2m}/{(n-1)}-n+2$. In this paper we prove a stronger result: For any graph with $n$ vertices and $m$ edges, we have $\\displaystyle q_n(G)\\ge {2m}/{(n-2)}-n+1 (n\\ge 6)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.3096","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"}