{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:HTM7TSFLPEERUWJKNQTDHKWR2I","short_pith_number":"pith:HTM7TSFL","schema_version":"1.0","canonical_sha256":"3cd9f9c8ab79091a592a6c2633aad1d2322ab8eb85f773a220a9f8ba3b3ead24","source":{"kind":"arxiv","id":"1412.2275","version":1},"attestation_state":"computed","paper":{"title":"The Signless Laplacian Estrada Index of Unicyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ahmad Gholami, Gholam Hossein Fath-Tabar, Hamid Reza Ellahi, Ramin Nasiri","submitted_at":"2014-12-06T20:23:52Z","abstract_excerpt":"For a graph $G$, the signless Laplacian Estrada index is defined as $SLEE(G)=\\sum^{n}_{i=1}e^{q^{}_i}$,where $q_1, q_2, \\dots, q_n$are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$ and then determine the unique unicyclic graph with maximum $SLEE$ among the unicyclic graphs on $n$ vertices with given diameter."},"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":"1412.2275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-12-06T20:23:52Z","cross_cats_sorted":[],"title_canon_sha256":"da042891725d76f8d58159959b17764707bfa98bd0c8090fe3b3ac5693ec9db3","abstract_canon_sha256":"d99d4d99a2aa17a782e3fcc9d61023ee42be45432c5e92165f503baf385f708c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:38:36.782345Z","signature_b64":"T3raDirK/c/vWzWVKLNnFGkrSSTW0TQyMCnkiJ2JS/BHAMaGHpGOPElEUc687kMDXXKI6/7rcW9b8jY/yPMlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3cd9f9c8ab79091a592a6c2633aad1d2322ab8eb85f773a220a9f8ba3b3ead24","last_reissued_at":"2026-05-18T00:38:36.781933Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:38:36.781933Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Signless Laplacian Estrada Index of Unicyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ahmad Gholami, Gholam Hossein Fath-Tabar, Hamid Reza Ellahi, Ramin Nasiri","submitted_at":"2014-12-06T20:23:52Z","abstract_excerpt":"For a graph $G$, the signless Laplacian Estrada index is defined as $SLEE(G)=\\sum^{n}_{i=1}e^{q^{}_i}$,where $q_1, q_2, \\dots, q_n$are the eigenvalues of the signless Laplacian matrix of $G$. In this paper, we first characterize the unicyclic graphs with the first two largest and smallest $SLEE$ and then determine the unique unicyclic graph with maximum $SLEE$ among the unicyclic graphs on $n$ vertices with given diameter."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.2275","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":"1412.2275","created_at":"2026-05-18T00:38:36.781990+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.2275v1","created_at":"2026-05-18T00:38:36.781990+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.2275","created_at":"2026-05-18T00:38:36.781990+00:00"},{"alias_kind":"pith_short_12","alias_value":"HTM7TSFLPEER","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_16","alias_value":"HTM7TSFLPEERUWJK","created_at":"2026-05-18T12:28:30.664211+00:00"},{"alias_kind":"pith_short_8","alias_value":"HTM7TSFL","created_at":"2026-05-18T12:28:30.664211+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/HTM7TSFLPEERUWJKNQTDHKWR2I","json":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I.json","graph_json":"https://pith.science/api/pith-number/HTM7TSFLPEERUWJKNQTDHKWR2I/graph.json","events_json":"https://pith.science/api/pith-number/HTM7TSFLPEERUWJKNQTDHKWR2I/events.json","paper":"https://pith.science/paper/HTM7TSFL"},"agent_actions":{"view_html":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I","download_json":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I.json","view_paper":"https://pith.science/paper/HTM7TSFL","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.2275&json=true","fetch_graph":"https://pith.science/api/pith-number/HTM7TSFLPEERUWJKNQTDHKWR2I/graph.json","fetch_events":"https://pith.science/api/pith-number/HTM7TSFLPEERUWJKNQTDHKWR2I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I/action/storage_attestation","attest_author":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I/action/author_attestation","sign_citation":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I/action/citation_signature","submit_replication":"https://pith.science/pith/HTM7TSFLPEERUWJKNQTDHKWR2I/action/replication_record"}},"created_at":"2026-05-18T00:38:36.781990+00:00","updated_at":"2026-05-18T00:38:36.781990+00:00"}