{"paper":{"title":"The largest $H$-eigenvalue and spectral radius of Laplacian tensor of non-odd-bipartite generalized power hypergraphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Murad-ul-Islam Khan, Ying-Ying Tan, Yi-Zheng Fan","submitted_at":"2015-10-08T01:24:40Z","abstract_excerpt":"Let $G$ be a simple graph or hypergraph, and let $A(G),L(G),Q(G)$ be the adjacency, Laplacian and signless Laplacian tensors of $G$ respectively. The largest $H$-eigenvalues (resp., the spectral radii) of $L(G),Q(G)$ are denoted respectively by $\\lambda_{\\max}^L(G), \\lambda_{\\max}^Q(G)$ (resp., $\\rho^L(G), \\rho^Q(G)$). For a connected non-bipartite simple graph $G$, $\\lambda_{\\max}^L(G)=\\rho^L(G) < \\rho^Q(G)$. But this does not hold for non-odd-bipartite hypergraphs. We will investigate this problem by considering a class of generalized power hypergraphs $G^{k,\\frac{k}{2}}$, which are construc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02178","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"}