{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:OFNIRW52JUNJTJLRYAVM3GJ36S","short_pith_number":"pith:OFNIRW52","schema_version":"1.0","canonical_sha256":"715a88dbba4d1a99a571c02acd993bf4a400aca26027cfc4ebfc0812557685d9","source":{"kind":"arxiv","id":"1901.10180","version":1},"attestation_state":"computed","paper":{"title":"On the distance $\\alpha$-spectral radius of a connected graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"B. Zhou, H.Y. Guo","submitted_at":"2019-01-29T08:54:21Z","abstract_excerpt":"For a connected graph $G$ and $\\alpha\\in [0,1)$, the distance $\\alpha$-spectral radius of $G$ is the spectral radius of the matrix $D_{\\alpha}(G)$ defined as $D_{\\alpha}(G)=\\alpha T(G)+(1-\\alpha)D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the distance matrix of $G$. We give bounds for the distance $\\alpha$-spectral radius, especially for graphs that are not transmission regular, propose some graft transformations that decrease or increase the distance $\\alpha$-spectral radius, and determine the unique graphs with minimum and maximum distance $\\alpha$-s"},"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":"1901.10180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2019-01-29T08:54:21Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"793a84da09131b8fe9927a7ceddf98e3a81f3b4723e8cc6bb822cb46ef9b2160","abstract_canon_sha256":"5e118b9e353bb7e5c1a4ea516cdb283afd50015233fe7d7e2353aa7e210886b8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:15.918979Z","signature_b64":"GUasJ939aG720f/Ypd2mMS/Egrz2Vn9FOhEQmMm3IVGEaYDyDyNhIvhR4SoOVdqTogfUE/sqb6bu4wX7SoJaBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"715a88dbba4d1a99a571c02acd993bf4a400aca26027cfc4ebfc0812557685d9","last_reissued_at":"2026-05-17T23:55:15.918536Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:15.918536Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the distance $\\alpha$-spectral radius of a connected graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"B. Zhou, H.Y. Guo","submitted_at":"2019-01-29T08:54:21Z","abstract_excerpt":"For a connected graph $G$ and $\\alpha\\in [0,1)$, the distance $\\alpha$-spectral radius of $G$ is the spectral radius of the matrix $D_{\\alpha}(G)$ defined as $D_{\\alpha}(G)=\\alpha T(G)+(1-\\alpha)D(G)$, where $T(G)$ is a diagonal matrix of vertex transmissions of $G$ and $D(G)$ is the distance matrix of $G$. We give bounds for the distance $\\alpha$-spectral radius, especially for graphs that are not transmission regular, propose some graft transformations that decrease or increase the distance $\\alpha$-spectral radius, and determine the unique graphs with minimum and maximum distance $\\alpha$-s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.10180","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":"1901.10180","created_at":"2026-05-17T23:55:15.918602+00:00"},{"alias_kind":"arxiv_version","alias_value":"1901.10180v1","created_at":"2026-05-17T23:55:15.918602+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1901.10180","created_at":"2026-05-17T23:55:15.918602+00:00"},{"alias_kind":"pith_short_12","alias_value":"OFNIRW52JUNJ","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_16","alias_value":"OFNIRW52JUNJTJLR","created_at":"2026-05-18T12:33:24.271573+00:00"},{"alias_kind":"pith_short_8","alias_value":"OFNIRW52","created_at":"2026-05-18T12:33:24.271573+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/OFNIRW52JUNJTJLRYAVM3GJ36S","json":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S.json","graph_json":"https://pith.science/api/pith-number/OFNIRW52JUNJTJLRYAVM3GJ36S/graph.json","events_json":"https://pith.science/api/pith-number/OFNIRW52JUNJTJLRYAVM3GJ36S/events.json","paper":"https://pith.science/paper/OFNIRW52"},"agent_actions":{"view_html":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S","download_json":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S.json","view_paper":"https://pith.science/paper/OFNIRW52","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1901.10180&json=true","fetch_graph":"https://pith.science/api/pith-number/OFNIRW52JUNJTJLRYAVM3GJ36S/graph.json","fetch_events":"https://pith.science/api/pith-number/OFNIRW52JUNJTJLRYAVM3GJ36S/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S/action/storage_attestation","attest_author":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S/action/author_attestation","sign_citation":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S/action/citation_signature","submit_replication":"https://pith.science/pith/OFNIRW52JUNJTJLRYAVM3GJ36S/action/replication_record"}},"created_at":"2026-05-17T23:55:15.918602+00:00","updated_at":"2026-05-17T23:55:15.918602+00:00"}