{"paper":{"title":"On ABC spectral radius of uniform hypergraphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Hongying Lin","submitted_at":"2023-03-27T06:09:46Z","abstract_excerpt":"Given a $k$-uniform hypergraph $G$ with vertex set $[n]$ and edge set $E(G)$, the ABC tensor $\\mathcal{ABC}(G)$ of $G$ is the $k$-order $n$-dimensional tensor with \\[\n  \\mathcal{ABC}(G)_{i_1, \\dots, i_k}=\n  \\begin{cases}\n  \\dfrac{1}{(k-1)!}\\sqrt[k]{\\dfrac{\\sum_{i\\in e}d_{i}-k}{\\prod_{i\\in e}d_{i}}} & \\mbox{if $e\\in E(G)$}\n  0 & \\mbox{otherwise} \\end{cases} \\] for $i_j\\in [n]$ with $j\\in [k]$, where $d_i$ is the degree of vertex $i$ in $G$. The ABC spectral radius of a uniform hypergraph is the spectral radius of its ABC tensor. We give tight lower and upper bounds for the ABC spectra radius, a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.14929","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.14929/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}