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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1510.02178","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-10-08T01:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"3c346e6acdc00f7eb3acc67e0f2cc88ce51ea3d9dc99fc04d45c6528571a170f","abstract_canon_sha256":"4b3c2e8bea752d934b36f11f43489dcd3fdcd856bd2c6ae8a5f4b354e9c21511"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:35:55.816332Z","signature_b64":"SLOmndEe6eL/qd2bgIA7uACa1SQP+7/1wwV6hHo2FCH9089rE6pGSjq4jDlMxa4aM9y1VJSBcNko/TisniPHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ddb1474a7c885d8bca256b291d1117a23ef5de5edaefbd2e3fcb78e106a049a","last_reissued_at":"2026-05-18T00:35:55.815950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:35:55.815950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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