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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 "},"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":"1404.5383","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-22T06:02:07Z","cross_cats_sorted":[],"title_canon_sha256":"86350b4cc65e0571ffa0dc88c83c6ab97b66bb1433964cab3d6aaed4abaa6448","abstract_canon_sha256":"00e3a4ee62cc38ad1be18efa48424774bc35b5900d1eebae057739767d703a25"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:28.378584Z","signature_b64":"JZ1G7TvSirU6NcB8ZnFMW7i9aszprIrLkcUjB3soyp7GaugA8x4Pr/TMF8yWHeVpksnV+n1J9EKQsyQviTm3Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9383cf91214d82b74505b30a58c2168d5dc3408e662d12a9add4aa00db777699","last_reissued_at":"2026-05-18T02:53:28.377873Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:28.377873Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $G$. 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