{"paper":{"title":"Lower bounds for Laplacian spread and relations with invariant parameters revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.SP","authors_text":"Enide Andrade, Jonnathan Rodr\\'iguez, Maria Aguieiras A. de Freitas, Mar\\'ia Robbiano","submitted_at":"2018-05-30T22:34:49Z","abstract_excerpt":"Let $G=\\left( V\\left( G\\right) ,E\\left( G\\right) \\right) $ be an $\\left( n,m\\right) $-graph and $X$ a nonempty proper subset of $V\\left( G\\right) $. Let $X^{c}=V\\left( G\\right) \\backslash X$.\\ The edge density of $X$ in $G$ is given by \\begin{equation*} \\rho _{G}\\left( X\\right) =\\frac{n\\left\\vert E_{X}\\left( G\\right) \\right\\vert }{\\left\\vert X\\right\\vert \\left\\vert X^{c}\\right\\vert }, \\end{equation*} where $E_{X}\\left( G\\right) \\ $ is the set of edges in $G$ with one end in $% X $ and the other in $X^{c}$. The Laplacian spread of a graph is the difference between the greatest Laplacian eigenva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.12250","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"}