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The minimum cardinality of a twin dominating set in $D$ is called the twin domination number of $D$ and is denoted by $\\gamma ^{*}(D)$.\n  The upper orientable twin domination number of a graph $G$ is $DOM^{*}(G)=\\max\\{ \\gamma ^{*}(D)|D \\ \\text{is an orientation of G} \\}.$ It has been conjectured that for the complete graph $K_n$ with $n\\geq 8$, $DOM^{*}(K_n)=\\left\\lceil \\frac{n+1}{2}\\right"},"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":"1702.00646","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-02-02T12:38:03Z","cross_cats_sorted":[],"title_canon_sha256":"d273d2182a1cbd710fef7f41765ed33e643efe5498bbb2b0adb723d1a6b5be76","abstract_canon_sha256":"5062f6f025887b562aacd73e82412a4e0fa4a852f2dddac75867759f500c671e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:44.562811Z","signature_b64":"s9aemh4p25H5mDWrwZmNgPzX3LoR7XvonbDQe+qTPzaP8I1rgEJqO6++Ehv62bhM6cKytarZLoCpSs0YU5w3BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2b89c6fa0cfe876e6a2a09c927798d2e2b2351ee86f4ad849415ab8b9af6bd9c","last_reissued_at":"2026-05-17T23:53:44.562416Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:44.562416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Twin domination number of Tournaments","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dorota Osula, Rita Zuazua","submitted_at":"2017-02-02T12:38:03Z","abstract_excerpt":"Let $D=(V,A)$ be a digraph. 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