{"paper":{"title":"The proof of a conjecture on largest Laplacian and signless Laplacian H-eigenvalues of uniform hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jiayu Shao, Liqun Qi, Xiying Yuan","submitted_at":"2015-06-09T13:22:49Z","abstract_excerpt":"Let $\\mathcal{A(}G\\mathcal{)},\\mathcal{L(}G\\mathcal{)}$ and $\\mathcal{Q(}% G\\mathcal{)}$ be the adjacency tensor, Laplacian tensor and signless Laplacian tensor of uniform hypergraph $G$, respectively. Denote by $\\lambda (\\mathcal{T})$ the largest H-eigenvalue of tensor $\\mathcal{T}$. Let $H$ be a uniform hypergraph, and $H^{\\prime}$ be obtained from $H$ by inserting a new vertex with degree one in each edge. We prove that $\\lambda(\\mathcal{Q(}% H^{\\prime}\\mathcal{)})\\leq\\lambda(\\mathcal{Q(}H\\mathcal{)}).$ Denote by $G^{k}$ the $k$th power hypergraph of an ordinary graph $G$ with maximum degre"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.03330","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"}