{"paper":{"title":"Maximizing the Smallest Eigenvalue of Grounded Laplacian Matrix","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Run Wang, Wei Li, Xiaotian Zhou, Zhongzhi Zhang","submitted_at":"2021-10-25T01:45:50Z","abstract_excerpt":"For a connected graph $\\mathcal{G}=(V,E)$ with $n$ nodes, $m$ edges, and Laplacian matrix $\\boldsymbol{{\\mathit{L}}}$, a grounded Laplacian matrix $\\boldsymbol{{\\mathit{L}}}(S)$ of $\\mathcal{G}$ is a $(n-k) \\times (n-k)$ principal submatrix of $\\boldsymbol{{\\mathit{L}}}$, obtained from $\\boldsymbol{{\\mathit{L}}}$ by deleting $k$ rows and columns corresponding to $k$ selected nodes forming a set $S\\subseteq V$. The smallest eigenvalue $\\lambda(S)$ of $\\boldsymbol{{\\mathit{L}}}(S)$ plays a pivotal role in various dynamics defined on $\\mathcal{G}$. For example, $\\lambda(S)$ characterizes the conv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2110.12576","kind":"arxiv","version":4},"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/2110.12576/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"}