{"paper":{"title":"Resolving dominating partitions in graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carmen Hernando, Ignacio M. Pelayo, Merc\\`e Mora","submitted_at":"2017-11-03T09:58:47Z","abstract_excerpt":"A partition $\\Pi=\\{S_1,\\ldots,S_k\\}$ of the vertex set of a connected graph $G$ is called a \\emph{resolving partition} of $G$ if for every pair of vertices $u$ and $v$, $d(u,S_j)\\neq d(v,S_j)$, for some part $S_j$. The \\emph{partition dimension} $\\beta_p(G)$ is the minimum cardinality of a resolving partition of $G$. A resolving partition $\\Pi$ is called \\emph{resolving dominating} if for every vertex $v$ of $G$, $d(v,S_j)=1$, for some part $S_j$ of $\\Pi$. The \\emph{dominating partition dimension} $\\eta_p(G)$ is the minimum cardinality of a resolving dominating partition of $G$.\n  In this pape"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01086","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"}