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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"},"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":"1506.03330","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-06-09T13:22:49Z","cross_cats_sorted":[],"title_canon_sha256":"938c6fbd0350033cd8e6968947be1ba491c655edea5dbeb88679dc4da835f8a4","abstract_canon_sha256":"c4ee4e97c6ace727753d8587dbf53dc7de78fcacf311c341122cccc668c13b83"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:55:25.000192Z","signature_b64":"iuZkGu762Y4WN1MFMfGwW6+6pemBISwd7PBseS+/Q8E8ld8nT7KozFGO6Ep/C6ddKk+0Un1uQKrxLjzcB+K7DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e0f300014fd3034003885f78d0ff35de7839e1b110fe039fde36464f3b532a4d","last_reissued_at":"2026-05-18T01:55:24.999623Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:55:24.999623Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1506.03330","created_at":"2026-05-18T01:55:24.999734+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.03330v1","created_at":"2026-05-18T01:55:24.999734+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.03330","created_at":"2026-05-18T01:55:24.999734+00:00"},{"alias_kind":"pith_short_12","alias_value":"4DZQAAKP2MBU","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_16","alias_value":"4DZQAAKP2MBUAA4I","created_at":"2026-05-18T12:29:05.191682+00:00"},{"alias_kind":"pith_short_8","alias_value":"4DZQAAKP","created_at":"2026-05-18T12:29:05.191682+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z","json":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z.json","graph_json":"https://pith.science/api/pith-number/4DZQAAKP2MBUAA4IL54NB7ZV3Z/graph.json","events_json":"https://pith.science/api/pith-number/4DZQAAKP2MBUAA4IL54NB7ZV3Z/events.json","paper":"https://pith.science/paper/4DZQAAKP"},"agent_actions":{"view_html":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z","download_json":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z.json","view_paper":"https://pith.science/paper/4DZQAAKP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.03330&json=true","fetch_graph":"https://pith.science/api/pith-number/4DZQAAKP2MBUAA4IL54NB7ZV3Z/graph.json","fetch_events":"https://pith.science/api/pith-number/4DZQAAKP2MBUAA4IL54NB7ZV3Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z/action/storage_attestation","attest_author":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z/action/author_attestation","sign_citation":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z/action/citation_signature","submit_replication":"https://pith.science/pith/4DZQAAKP2MBUAA4IL54NB7ZV3Z/action/replication_record"}},"created_at":"2026-05-18T01:55:24.999734+00:00","updated_at":"2026-05-18T01:55:24.999734+00:00"}