{"paper":{"title":"Computing all Laplacian H-eigenvalues for a k-uniform loose path of length three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Junjie Yue, Liping Zhang","submitted_at":"2018-05-14T02:21:46Z","abstract_excerpt":"The spectral theory of Laplacian tensor is an important tool for revealing some important properties of a hypergraph. It is meaningful to compute all Laplacian H-eigenvalues for some special $k$-uniform hypergraphs. For an odd-uniform loose path of length three, the Laplacian H-spectrum has been studied. However, all Laplacian H-eigenvalues of the class of loose paths have not been found out. In this paper, we compute all Laplacian H-eigenvalues for the class of loose paths. We show that the number of Laplacian H-eigenvalues of an odd(even)-uniform loose path with length three is $7$($14$). So"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.05798","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"}