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Also, a subset $D$ of a graph $G$ is a $[ 1 , 2 ] $-set if, each vertex $v \\in V \\setminus D$ is adjacent to either one or two vertices in $D$ and the minimum cardinality of $[ 1 , 2 ] $-dominating set of $G$, is denoted by $\\gamma_{[1,2]}(G)$. Chang's conjecture says that for every $16 \\leq m \\leq n$, $\\gamma(G_{m,n})= \\left \\lfloor\\frac{(n+2)(m+2)}"},"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":"1707.06471","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DM","submitted_at":"2017-07-20T12:24:40Z","cross_cats_sorted":[],"title_canon_sha256":"5cebf5ce1c9e3c8d4165d2987c414c22db8c131ca6f416360d9a5c199499071b","abstract_canon_sha256":"2aba336b9c2b08af637154ebe55a89036dc4ac360f8ad4f914e058f570abb585"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:56.360276Z","signature_b64":"rVhD0sJzbLcj0+f+TDTZ64joq7/Dk65DJJDIvpOvIYCKWeW2h/yWBYDK4yY+3jNnNOu2IqeRjjaWV0IMdCUVBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"72c4d56daec8912b392a58f14e182c6c7b809c8f98901133ed2bfa4614e2888d","last_reissued_at":"2026-05-18T00:20:56.359761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:56.359761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Explicit Construction of Optimal Dominating Sets in Grid","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DM","authors_text":"M. 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