{"paper":{"title":"On the $\\alpha$-spectral radius of uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Haiyan Guo","submitted_at":"2018-07-21T09:33:32Z","abstract_excerpt":"For $0\\le\\alpha<1$ and a uniform hypergraph $G$, the $\\alpha$-spectral radius of $G$ is the largest $H$-eigenvalue of $\\alpha \\mathcal{D}(G) +(1-\\alpha)\\mathcal{A}(G)$, where $\\mathcal{D}(G)$ and $\\mathcal{A}(G)$ are the diagonal tensor of degrees and the adjacency tensor of $G$, respectively. We give upper bounds for the $\\alpha$-spectral radius of a uniform hypergraph, propose some transformations that increase the $\\alpha$-spectral radius, and determine the unique hypergraphs with maximum $\\alpha$-spectral radius in some classes of uniform hypergraphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08112","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"}