{"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. We study locating and identifying codes in the circulant networks"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4660","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"}