{"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. In this paper we obtain upper and lower bounds of $I_d^t(\\mathcal{H})$ f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09594","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"}