{"paper":{"title":"On the Partition Dimension of Circulant Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bharati Rajan, Cyriac Grigorious, Mirka Miller, Paul Manuel, Sudeep Stephen","submitted_at":"2015-07-19T02:36:43Z","abstract_excerpt":"For a vertex $v$ of a connected graph $G(V,E)$ and a subset $S$ of $V$, the distance between $v$ and $S$ is defined by $d(v,S)=min\\{d(v,x):x \\in S \\}.$ For an ordered \\emph{k}-partition $\\Pi=\\{S_1,S_2\\ldots S_k\\}$ of $V$, the representation of $v$ with respect to $\\Pi$ is the $k$-vector $r(v|\\Pi) =(d(v,S_1),d(v,S_2)\\ldots d(v,S_k)).$ The $k$-partition $\\Pi$ is a resolving partition if the $k$-vectors $r(v|\\Pi)$, $v \\in V$ are distinct. The minimum $k$ for which there is a resolving $k$-partition of $V$ is the \\emph{partition dimension} of $G$. Salman et al.{\\rm\\cite{SaJaCh12}} claimed that \\em"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.05239","kind":"arxiv","version":2},"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"}