{"paper":{"title":"On the irregularity of uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erfang Shan, Lele Liu, Liying Kang","submitted_at":"2018-02-06T15:29:51Z","abstract_excerpt":"Let $H$ be an $r$-uniform hypergraph on $n$ vertices and $m$ edges, and let $d_i$ be the degree of $i\\in V(H)$. Denote by $\\varepsilon(H)$ the difference of the spectral radius of $H$ and the average degree of $H$. Also, denote \\[ s(H)=\\sum_{i\\in V(H)}\\left|d_i-\\frac{rm}{n}\\right|,~ v(H)=\\frac{1}{n}\\sum_{i\\in V(H)}d_i^{\\frac{r}{r-1}}-\\left(\\frac{rm}{n}\\right)^{\\frac{r}{r-1}}. \\] In this paper, we investigate the irregularity of $r$-uniform hypergraph $H$ with respect to $\\varepsilon(H)$, $s(H)$ and $v(H)$, which extend relevant results to uniform hypergraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.02146","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"}