{"paper":{"title":"Randi\\'c energy and Randi\\'c eigenvalues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jianfeng Wang, Xueliang Li","submitted_at":"2014-04-22T06:02:07Z","abstract_excerpt":"Let $G$ be a graph of order $n$, and $d_i$ the degree of a vertex $v_i$ of $G$. The Randi\\'c matrix ${\\bf R}=(r_{ij})$ of $G$ is defined by $r_{ij} = 1 / \\sqrt{d_jd_j}$ if the vertices $v_i$ and $v_j$ are adjacent in $G$ and $r_{ij}=0$ otherwise. The normalized signless Laplacian matrix $\\mathcal{Q}$ is defined as $\\mathcal{Q} =I+\\bf{R}$, where $I$ is the identity matrix. The Randi\\'c energy is the sum of absolute values of the eigenvalues of $\\bf{R}$. In this paper, we find a relation between the normalized signless Laplacian eigenvalues of $G$ and the Randi\\'c energy of its subdivided graph "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5383","kind":"arxiv","version":2},"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"}