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A set S \\subseteq V(G) is called a locating code in G, if the sets S \\cap N[u] where u \\in V(G) \\setminus S are all nonempty and distinct. A set S \\subseteq V(G) is called an identifying code in G, if the sets S\\cap N[u] where u\\in V(G) are all nonempty and distinct. We study locating and identifying codes in the circulant networks"},"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":"1207.4660","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-07-19T13:27:05Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"5e6fe9fedfbfba1ccd9f3b63b670ee8dc8763fba7bd34c9ba2f05da9bbaf80d2","abstract_canon_sha256":"a858564271daed17bf7edb78af77f253570af641cddcb8a12c38798cb8187baa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:50:36.224235Z","signature_b64":"ek33ZBWKpIiM3CpQ/Q99n02Z+4eX7aKszRTaVSWAS7AMI3O3PCb4WYThrgutnRdJp4T9TZrb73Jn4FalO5o0CA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d77a383ededd484ff167b24f021301aa6596a6c08c8e9c0699445b9e66718d4","last_reissued_at":"2026-05-18T03:50:36.223529Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:50:36.223529Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Locating and Identifying Codes in Circulant Networks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"L. Niepel, M. Ghebleh","submitted_at":"2012-07-19T13:27:05Z","abstract_excerpt":"A set S of vertices of a graph G is a dominating set of G if every vertex u of G is either in S or it has a neighbour in S. In other words, S is dominating if the sets S\\cap N[u] where u \\in V(G) and N[u] denotes the closed neighbourhood of u in G, are all nonempty. A set S \\subseteq V(G) is called a locating code in G, if the sets S \\cap N[u] where u \\in V(G) \\setminus S are all nonempty and distinct. A set S \\subseteq V(G) is called an identifying code in G, if the sets S\\cap N[u] where u\\in V(G) are all nonempty and distinct. 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