{"paper":{"title":"The Algebraic Connectivity of a Graph and its Complement","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"B. Afshari, B. Mohar, M.J. Moghaddamzadeh, S. Akbari","submitted_at":"2018-06-18T15:27:18Z","abstract_excerpt":"For a graph $G$, let $\\lambda_2(G)$ denote its second smallest Laplacian eigenvalue. It was conjectured that $\\lambda_2(G) + \\lambda_2(\\overline G) \\ge 1$, where $\\overline G$ is the complement of $G$. In this paper, it is shown that $\\max\\{\\lambda_2(G), \\lambda_2(\\overline G)\\} \\ge 2/5$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.06770","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"}