{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:37HXFJX6JRVNTQLDOM6WWI7USH","short_pith_number":"pith:37HXFJX6","schema_version":"1.0","canonical_sha256":"dfcf72a6fe4c6ad9c163733d6b23f491e53ebf539375cb69b11cd54483277a6e","source":{"kind":"arxiv","id":"1612.02643","version":1},"attestation_state":"computed","paper":{"title":"The $p$-spectral radius of the Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos Hoppen, Eliseu Fritscher, Elizandro Max Borba, Sebastian Richter","submitted_at":"2016-12-08T13:45:56Z","abstract_excerpt":"The $p$-spectral radius of a graph $G=(V,E)$ with adjacency matrix $A$ is defined as $\\lambda^{(p)}(G)=\\max \\{x^TAx : \\|x\\|_p=1 \\}$. This parameter shows remarkable connections with graph invariants, and has been used to generalize some extremal problems. In this work, we extend this approach to the Laplacian matrix $L$, and define the $p$-spectral radius of the Laplacian as $\\mu^{(p)}(G)=\\max \\{x^TLx : \\|x\\|_p=1 \\}$. We show that $\\mu^{(p)}(G)$ relates to invariants such as maximum degree and size of a maximum cut. We also show properties of $\\mu^{(p)}(G)$ as a function of $p$, and a upper bo"},"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":"1612.02643","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-12-08T13:45:56Z","cross_cats_sorted":[],"title_canon_sha256":"50e861c110bf45abdc1ec30dcfdab4ce9a71aa8ac92e619043406a01dfa7331a","abstract_canon_sha256":"723787cd7b576b43d819ef122590eab7229b54b25c4901c852130c896ea561f3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:55:33.187954Z","signature_b64":"PywmXq7IflU160NNYhh3eXcQjpktaZdLYn/8th43ChXwJaT7H1KMlOcJHe2aS6mjcf3/aqBo+qASII3AGOBZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dfcf72a6fe4c6ad9c163733d6b23f491e53ebf539375cb69b11cd54483277a6e","last_reissued_at":"2026-05-18T00:55:33.187497Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:55:33.187497Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The $p$-spectral radius of the Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos Hoppen, Eliseu Fritscher, Elizandro Max Borba, Sebastian Richter","submitted_at":"2016-12-08T13:45:56Z","abstract_excerpt":"The $p$-spectral radius of a graph $G=(V,E)$ with adjacency matrix $A$ is defined as $\\lambda^{(p)}(G)=\\max \\{x^TAx : \\|x\\|_p=1 \\}$. This parameter shows remarkable connections with graph invariants, and has been used to generalize some extremal problems. In this work, we extend this approach to the Laplacian matrix $L$, and define the $p$-spectral radius of the Laplacian as $\\mu^{(p)}(G)=\\max \\{x^TLx : \\|x\\|_p=1 \\}$. We show that $\\mu^{(p)}(G)$ relates to invariants such as maximum degree and size of a maximum cut. We also show properties of $\\mu^{(p)}(G)$ as a function of $p$, and a upper bo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.02643","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":"1612.02643","created_at":"2026-05-18T00:55:33.187567+00:00"},{"alias_kind":"arxiv_version","alias_value":"1612.02643v1","created_at":"2026-05-18T00:55:33.187567+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1612.02643","created_at":"2026-05-18T00:55:33.187567+00:00"},{"alias_kind":"pith_short_12","alias_value":"37HXFJX6JRVN","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_16","alias_value":"37HXFJX6JRVNTQLD","created_at":"2026-05-18T12:29:55.572404+00:00"},{"alias_kind":"pith_short_8","alias_value":"37HXFJX6","created_at":"2026-05-18T12:29:55.572404+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/37HXFJX6JRVNTQLDOM6WWI7USH","json":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH.json","graph_json":"https://pith.science/api/pith-number/37HXFJX6JRVNTQLDOM6WWI7USH/graph.json","events_json":"https://pith.science/api/pith-number/37HXFJX6JRVNTQLDOM6WWI7USH/events.json","paper":"https://pith.science/paper/37HXFJX6"},"agent_actions":{"view_html":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH","download_json":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH.json","view_paper":"https://pith.science/paper/37HXFJX6","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1612.02643&json=true","fetch_graph":"https://pith.science/api/pith-number/37HXFJX6JRVNTQLDOM6WWI7USH/graph.json","fetch_events":"https://pith.science/api/pith-number/37HXFJX6JRVNTQLDOM6WWI7USH/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH/action/timestamp_anchor","attest_storage":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH/action/storage_attestation","attest_author":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH/action/author_attestation","sign_citation":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH/action/citation_signature","submit_replication":"https://pith.science/pith/37HXFJX6JRVNTQLDOM6WWI7USH/action/replication_record"}},"created_at":"2026-05-18T00:55:33.187567+00:00","updated_at":"2026-05-18T00:55:33.187567+00:00"}