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The $t$-th graph entropy based on degrees of $\\mathcal{H}$ is defined as $$ I_d^t(\\mathcal{H}) =-\\sum_{i=1}^{n}\\left(\\frac{d_i^{t}}{\\sum_{j=1}^{n}d_j^{t}}\\log\\frac{d_i^{t}}{\\sum_{j=1}^{n}d_j^{t}}\\right) =\\log\\left(\\sum_{i=1}^{n}d_i^{t}\\right)-\\sum_{i=1}^{n}\\left(\\frac{d_i^{t}}{\\sum_{j=1}^{n}d_j^{t}}\\log d_i^{t}\\right), $$ where $t$ is a real number and the logarithm is taken to the base two. In this paper we obtain upper and lower bounds of $I_d^t(\\mathcal{H})$ f"},"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":"1709.09594","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-09-27T15:52:27Z","cross_cats_sorted":[],"title_canon_sha256":"50c92f54efedf4f4064b1b761031f4ee8322fb98b1854e91331033a20a5e74ce","abstract_canon_sha256":"0a96b9f841305a225aa88216330a02a80eb1b71a0a7ca78254492800797a3596"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:34:11.208508Z","signature_b64":"xYE7JtmmbvV/e6EqLEAxitjTnJ0EZUNYvfn+rq0hDA1psPS25FeTn2oogZL/De9b4fpb3ZlXBTHGD3iGiwHSDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d5984d2ec5ead698ee93d32a86840f683c52fdfc6ee98ad4be530ab04dd3bff0","last_reissued_at":"2026-05-18T00:34:11.207868Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:34:11.207868Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremality of graph entropy based on degrees of uniform hypergraphs with few edges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Hu, Shenggui Zhang, Xiaogang Liu, Xueliang Li","submitted_at":"2017-09-27T15:52:27Z","abstract_excerpt":"Let $\\mathcal{H}$ be a hypergraph with $n$ vertices. Suppose that $d_1,d_2,\\ldots,d_n$ are degrees of the vertices of $\\mathcal{H}$. The $t$-th graph entropy based on degrees of $\\mathcal{H}$ is defined as $$ I_d^t(\\mathcal{H}) =-\\sum_{i=1}^{n}\\left(\\frac{d_i^{t}}{\\sum_{j=1}^{n}d_j^{t}}\\log\\frac{d_i^{t}}{\\sum_{j=1}^{n}d_j^{t}}\\right) =\\log\\left(\\sum_{i=1}^{n}d_i^{t}\\right)-\\sum_{i=1}^{n}\\left(\\frac{d_i^{t}}{\\sum_{j=1}^{n}d_j^{t}}\\log d_i^{t}\\right), $$ where $t$ is a real number and the logarithm is taken to the base two. 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