{"paper":{"title":"Identifying Codes on Directed De Bruijn Graphs","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Debra Boutin, Mikko Pelto, Victoria Horan Goliber","submitted_at":"2014-12-18T12:59:54Z","abstract_excerpt":"For a directed graph $G$, a $t$-identifying code is a subset $S\\subseteq V(G)$ with the property that for each vertex $v\\in V(G)$ the set of vertices of $S$ reachable from $v$ by a directed path of length at most $t$ is both non-empty and unique. A graph is called {\\it $t$-identifiable} if there exists a $t$-identifying code. This paper shows that the de~Bruijn graph $\\vec{\\mathcal{B}}(d,n)$ is $t$-identifiable if and only if $n \\geq 2t-1$. It is also shown that a $t$-identifying code for $t$-identifiable de~Bruijn graphs must contain at least $d^{n-1}(d-1)$ vertices, and constructions are giv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5842","kind":"arxiv","version":3},"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"}