{"paper":{"title":"Bounds and power means for the general Randic index","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Clive Elphick, Pawel Wocjan","submitted_at":"2015-08-31T18:36:09Z","abstract_excerpt":"We review bounds for the general Randi\\'c index, $R_{\\alpha} = \\sum_{ij \\in E} (d_i d_j)^\\alpha$, and use the power mean inequality to prove, for example, that $R_\\alpha \\ge m\\lambda^{2\\alpha}$ for $\\alpha < 0$, where $\\lambda$ is the spectral radius of a graph. This enables us to strengthen various known lower and upper bounds for $R_\\alpha$ and to generalise a non-spectral bound due to Bollob\\'as \\emph{et al}. We also prove that the zeroth-order general Randi\\'c index, $Q_\\alpha = \\sum_{i \\in V} d_i^\\alpha \\ge n\\lambda^\\alpha$ for $\\alpha < 0$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07950","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"}