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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1012.4856","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-12-22T01:48:52Z","cross_cats_sorted":[],"title_canon_sha256":"2ab520e39ea0e6bc02a066a59a640ae151e01de24dfc06afa2ad5be27571570e","abstract_canon_sha256":"564e998e93106caa53c87bf2374c589b32fa421ce294a3373c214bbb64219f27"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:45.120686Z","signature_b64":"iPt4pASsRM95mjTicLRDiEKCoic9Jl3GRsprCuBDM4VMjKCcU1fMrvRbsi+awvObSTrh85CaIqJQJj9tTJyJCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7eac5b92a3d58d84984df7435724293a3ae7829b0a5e498c86afd2176b1a5c2a","last_reissued_at":"2026-05-18T04:32:45.120244Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:45.120244Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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