{"paper":{"title":"On the Randi\\'{c} index and conditional parameters of a graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"J. A. Rodr\\'iguez, J. M. Sigarreta","submitted_at":"2013-11-28T13:44:02Z","abstract_excerpt":"The aim of this paper is to study some parameters of simple graphs related with the degree of the vertices. So, our main tool is the $n\\times n$ matrix ${\\cal A}$ whose ($i,j$)-entry is $$ a_{ij}= \\left\\lbrace \\begin{array}{ll}\n  \\frac{1}{\\sqrt{\\delta_i\\delta_j}} & {\\rm if }\\quad v_i\\sim v_j ;\n  \\\\ 0 & {\\rm otherwise,} \\end{array}\n  \\right. $$ where $\\delta_i$ denotes the degree of the vertex $v_i$. We study the Randi\\'{c} index and some interesting particular cases of conditional excess, conditional Wiener index, and conditional diameter. In particular, using the matrix ${\\cal A}$ or its eige"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.7316","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"}