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Caporossi et al. conjecture that the unicyclic graph with maximal energy is $P_n^6$ for $n=8,12,14$ and $n\\geq 16$. In``Y. Hou, I. Gutman and C. Woo, Unicyclic graphs with maximal energy, {\\it Linear Algebra Appl.} {\\bf 356}(2002), 27--36\", the authors proved that $E(P_n^6)$ is maximal within the class of the unicyclic biparti"},"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":"1010.6129","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-10-29T06:03:20Z","cross_cats_sorted":[],"title_canon_sha256":"fc3067ce2ad9051ea5a11a75c2933931de7b09941308b77fed20ac82ae70a050","abstract_canon_sha256":"6507cdb985bcd85fd5db8226662b9c78ed2fbb15555d0e9f32e0544098c60f92"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:38:07.438485Z","signature_b64":"ZfZcrpMeDXwn+VI1JArTpMhkOr5fXdD1G8GvwicGbqPZlAyqhvpd+Ym6o2xDh5zXo4zciPbc92KffN/I/9cbCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"92fdf935af49b67e3793fff62996d688bfa6a89eb265db93fc7e888aa920fc45","last_reissued_at":"2026-05-18T04:38:07.438061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:38:07.438061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Complete solution to a problem on the maximal energy of unicyclic bipartite graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bofeng Huo, Xueliang Li, Yongtang Shi","submitted_at":"2010-10-29T06:03:20Z","abstract_excerpt":"The energy of a simple graph $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Denote by $C_n$ the cycle, and $P_n^{6}$ the unicyclic graph obtained by connecting a vertex of $C_6$ with a leaf of $P_{n-6}$\\,. Caporossi et al. conjecture that the unicyclic graph with maximal energy is $P_n^6$ for $n=8,12,14$ and $n\\geq 16$. In``Y. Hou, I. Gutman and C. Woo, Unicyclic graphs with maximal energy, {\\it Linear Algebra Appl.} {\\bf 356}(2002), 27--36\", the authors proved that $E(P_n^6)$ is maximal within the class of the unicyclic biparti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6129","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":"1010.6129","created_at":"2026-05-18T04:38:07.438125+00:00"},{"alias_kind":"arxiv_version","alias_value":"1010.6129v1","created_at":"2026-05-18T04:38:07.438125+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.6129","created_at":"2026-05-18T04:38:07.438125+00:00"},{"alias_kind":"pith_short_12","alias_value":"SL67SNNPJG3H","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_16","alias_value":"SL67SNNPJG3H4N4T","created_at":"2026-05-18T12:26:13.927090+00:00"},{"alias_kind":"pith_short_8","alias_value":"SL67SNNP","created_at":"2026-05-18T12:26:13.927090+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/SL67SNNPJG3H4N4T773CTFWWRC","json":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC.json","graph_json":"https://pith.science/api/pith-number/SL67SNNPJG3H4N4T773CTFWWRC/graph.json","events_json":"https://pith.science/api/pith-number/SL67SNNPJG3H4N4T773CTFWWRC/events.json","paper":"https://pith.science/paper/SL67SNNP"},"agent_actions":{"view_html":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC","download_json":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC.json","view_paper":"https://pith.science/paper/SL67SNNP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1010.6129&json=true","fetch_graph":"https://pith.science/api/pith-number/SL67SNNPJG3H4N4T773CTFWWRC/graph.json","fetch_events":"https://pith.science/api/pith-number/SL67SNNPJG3H4N4T773CTFWWRC/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC/action/storage_attestation","attest_author":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC/action/author_attestation","sign_citation":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC/action/citation_signature","submit_replication":"https://pith.science/pith/SL67SNNPJG3H4N4T773CTFWWRC/action/replication_record"}},"created_at":"2026-05-18T04:38:07.438125+00:00","updated_at":"2026-05-18T04:38:07.438125+00:00"}