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In this article we give, in general, the value of $\\gamma(C_m\\Box C_n)$ when $m\\equiv 2$ $(mod\\: 3)$ and improve the known lower bound for most of the remaining cases. We also disprove the conjectured formula for the case $m$ $\\equiv 0$ $(mod\\: 3)$ appearing in \\cite{}"},"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":"1205.5537","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-05-24T19:25:40Z","cross_cats_sorted":[],"title_canon_sha256":"39f53afbbd720541bfb71adb300a0421e20b354e2427547f66766e5bb1949f70","abstract_canon_sha256":"78e1189af878b31179ae23f8ad688d3ec98b2293a5b171db8e2d354e3d081105"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:55:00.862441Z","signature_b64":"QY0KCRd6W8zrWeb7kY41Ebku+B0n7Gwe2pP63obEnrpWQasoKNpo4oAyWFdP2a+VvgIDZPc7Xuazu48ElZJHAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"49dd96eb4b93f8df5596d29f853ee55bcbd19f99e41b7835430bce158b2ab48c","last_reissued_at":"2026-05-18T03:55:00.861863Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:55:00.861863Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On domination of Cartesian product of directed cycles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Michel Mollard (IF)","submitted_at":"2012-05-24T19:25:40Z","abstract_excerpt":"Let $\\gamma(C_m\\Box C_n)$ be the domination number of the Cartesian product of directed cycles $C_m$ and $C_n$ for $m,n\\geq2$. 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