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The skew energy of an oriented graph $G^{\\sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{\\sigma})$. For any positive integer $d$ with $3\\leq d\\leq n-3$, we determine the graph with minimal skew energy among all oriented bicyclic graphs that contain no vertex disjoint odd cycle of lengths $s$ and $l$ with $s+l\\equiv 2(mod 4)$ on $n$ vertices with a given diameter $d$."},"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":"1610.06644","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2016-10-21T01:50:44Z","cross_cats_sorted":[],"title_canon_sha256":"0f2b26cd117b6da1920cf5e4ddd2b8b1d7254bac3d6d4b4ae893f356cb09c598","abstract_canon_sha256":"e583d3790d06c27040f4945eb5da4f5dbaf5ffc147c531ad8d8bc7ce5d19746a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:01:37.123967Z","signature_b64":"UBp7PeUOITtFei5kfLOrPYYABP14jhBmSmVvrwucvctghPffx9mP7h03hGWv91iSTRiGlxQRaUvIGT2lz/bWAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7920f11e6eb1560084c5362273707cdd1c49d99de1c102a42184048f5484d929","last_reissued_at":"2026-05-18T01:01:37.123335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:01:37.123335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Minimal Skew energy of oriented bicyclic graphs with a given diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Ligong Wang, Xiangxiang Liu","submitted_at":"2016-10-21T01:50:44Z","abstract_excerpt":"Let $S(G^{\\sigma})$ be the skew-adjacency matrix of the oriented graph $G^{\\sigma}$, which is obtained from a simple undirected graph $G$ by assigning an orientation $\\sigma$ to each of its edges. The skew energy of an oriented graph $G^{\\sigma}$ is defined as the sum of absolute values of all eigenvalues of $S(G^{\\sigma})$. For any positive integer $d$ with $3\\leq d\\leq n-3$, we determine the graph with minimal skew energy among all oriented bicyclic graphs that contain no vertex disjoint odd cycle of lengths $s$ and $l$ with $s+l\\equiv 2(mod 4)$ on $n$ vertices with a given diameter $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06644","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":"1610.06644","created_at":"2026-05-18T01:01:37.123429+00:00"},{"alias_kind":"arxiv_version","alias_value":"1610.06644v1","created_at":"2026-05-18T01:01:37.123429+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1610.06644","created_at":"2026-05-18T01:01:37.123429+00:00"},{"alias_kind":"pith_short_12","alias_value":"PEQPCHTOWFLA","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_16","alias_value":"PEQPCHTOWFLABBGF","created_at":"2026-05-18T12:30:39.010887+00:00"},{"alias_kind":"pith_short_8","alias_value":"PEQPCHTO","created_at":"2026-05-18T12:30:39.010887+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/PEQPCHTOWFLABBGFGYRHG4D43U","json":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U.json","graph_json":"https://pith.science/api/pith-number/PEQPCHTOWFLABBGFGYRHG4D43U/graph.json","events_json":"https://pith.science/api/pith-number/PEQPCHTOWFLABBGFGYRHG4D43U/events.json","paper":"https://pith.science/paper/PEQPCHTO"},"agent_actions":{"view_html":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U","download_json":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U.json","view_paper":"https://pith.science/paper/PEQPCHTO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1610.06644&json=true","fetch_graph":"https://pith.science/api/pith-number/PEQPCHTOWFLABBGFGYRHG4D43U/graph.json","fetch_events":"https://pith.science/api/pith-number/PEQPCHTOWFLABBGFGYRHG4D43U/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U/action/timestamp_anchor","attest_storage":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U/action/storage_attestation","attest_author":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U/action/author_attestation","sign_citation":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U/action/citation_signature","submit_replication":"https://pith.science/pith/PEQPCHTOWFLABBGFGYRHG4D43U/action/replication_record"}},"created_at":"2026-05-18T01:01:37.123429+00:00","updated_at":"2026-05-18T01:01:37.123429+00:00"}