{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:B5SJG35FZNYD6OYQXSCZHN634I","short_pith_number":"pith:B5SJG35F","schema_version":"1.0","canonical_sha256":"0f64936fa5cb703f3b10bc8593b7dbe22cd3c8982a97f35a2bec65d22e2e3024","source":{"kind":"arxiv","id":"1103.4814","version":1},"attestation_state":"computed","paper":{"title":"On Laplacian like energy of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Aleksandar Ilic, Djordje Krtinic, Milovan Ilic","submitted_at":"2011-03-24T17:10:02Z","abstract_excerpt":"Let $G$ be a simple undirected $n$-vertex graph with the characteristic polynomial of its Laplacian matrix $L(G)$, $\\det (\\lambda I - L (G))=\\sum_{k = 0}^n (-1)^k c_k \\lambda^{n - k}$. Laplacian--like energy of a graph is newly proposed graph invariant, defined as the sum of square roots of Laplacian eigenvalues. For bipartite graphs, the Laplacian--like energy coincides with the recently defined incidence energy $IE (G)$ of a graph. In [D. Stevanovi\\' c, \\textit{Laplacian--like energy of trees}, MATCH Commun. Math. Comput. Chem. 61 (2009), 407--417.] the author introduced a partial ordering o"},"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":"1103.4814","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2011-03-24T17:10:02Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fec009eb22db05229e0cf051017b597f773e51f09e90012eab13b77ea7d0d53f","abstract_canon_sha256":"695783cd06b05b1fd7f26677085fbfd87bcdd017f98cb4265fbf77a1fa26a87f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:26:00.841271Z","signature_b64":"ffL+xOIf/4cRA/RMksUQLVWXc5yN23ln+rJ0fTQx/yEMCpCVaQ14jnaXjhltFziBfCREMLXpMaPvEGGfpGVICA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0f64936fa5cb703f3b10bc8593b7dbe22cd3c8982a97f35a2bec65d22e2e3024","last_reissued_at":"2026-05-18T04:26:00.840819Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:26:00.840819Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Laplacian like energy of trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.CA","authors_text":"Aleksandar Ilic, Djordje Krtinic, Milovan Ilic","submitted_at":"2011-03-24T17:10:02Z","abstract_excerpt":"Let $G$ be a simple undirected $n$-vertex graph with the characteristic polynomial of its Laplacian matrix $L(G)$, $\\det (\\lambda I - L (G))=\\sum_{k = 0}^n (-1)^k c_k \\lambda^{n - k}$. Laplacian--like energy of a graph is newly proposed graph invariant, defined as the sum of square roots of Laplacian eigenvalues. For bipartite graphs, the Laplacian--like energy coincides with the recently defined incidence energy $IE (G)$ of a graph. In [D. Stevanovi\\' c, \\textit{Laplacian--like energy of trees}, MATCH Commun. Math. Comput. Chem. 61 (2009), 407--417.] the author introduced a partial ordering o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4814","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":"1103.4814","created_at":"2026-05-18T04:26:00.840892+00:00"},{"alias_kind":"arxiv_version","alias_value":"1103.4814v1","created_at":"2026-05-18T04:26:00.840892+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.4814","created_at":"2026-05-18T04:26:00.840892+00:00"},{"alias_kind":"pith_short_12","alias_value":"B5SJG35FZNYD","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_16","alias_value":"B5SJG35FZNYD6OYQ","created_at":"2026-05-18T12:26:24.575870+00:00"},{"alias_kind":"pith_short_8","alias_value":"B5SJG35F","created_at":"2026-05-18T12:26:24.575870+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/B5SJG35FZNYD6OYQXSCZHN634I","json":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I.json","graph_json":"https://pith.science/api/pith-number/B5SJG35FZNYD6OYQXSCZHN634I/graph.json","events_json":"https://pith.science/api/pith-number/B5SJG35FZNYD6OYQXSCZHN634I/events.json","paper":"https://pith.science/paper/B5SJG35F"},"agent_actions":{"view_html":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I","download_json":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I.json","view_paper":"https://pith.science/paper/B5SJG35F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1103.4814&json=true","fetch_graph":"https://pith.science/api/pith-number/B5SJG35FZNYD6OYQXSCZHN634I/graph.json","fetch_events":"https://pith.science/api/pith-number/B5SJG35FZNYD6OYQXSCZHN634I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I/action/storage_attestation","attest_author":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I/action/author_attestation","sign_citation":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I/action/citation_signature","submit_replication":"https://pith.science/pith/B5SJG35FZNYD6OYQXSCZHN634I/action/replication_record"}},"created_at":"2026-05-18T04:26:00.840892+00:00","updated_at":"2026-05-18T04:26:00.840892+00:00"}