{"paper":{"title":"Note on a relation between Randic index and algebraic connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Xueliang Li, Yongtang Shi","submitted_at":"2010-12-22T01:48:52Z","abstract_excerpt":"A conjecture of AutoGraphiX on the relation between the Randi\\'c index $R$ and the algebraic connectivity $a$ of a connected graph $G$ is: $$\\frac R a\\leq (\\frac{n-3+2\\sqrt{2}}{2})/(2(1- \\cos {\\frac{\\pi}{n}})) $$ with equality if and only if $G$ is $P_n$, which was proposed by Aouchiche and Hansen [M. Aouchiche and P. Hansen, A survey of automated conjectures in spectral graph theory, {\\it Linear Algebra Appl.} {\\bf 432}(2010), 2293--2322]. We prove that the conjecture holds for all trees and all connected graphs with edge connectivity $\\kappa'(G)\\geq 2$, and if $\\kappa'(G)=1$, the conjecture "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.4856","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"}