{"paper":{"title":"On the adjacency dimension of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Estrada-Moreno, J. A. Rodriguez-Velazquez, Y. Ramirez-Cruz","submitted_at":"2015-01-19T21:22:50Z","abstract_excerpt":"A generator of a metric space is a set $S$ of points in the space with the property that every point of the space is uniquely determined by its distances from the elements of $S$. Given a simple graph $G=(V,E)$, we define the distance function $d_{G,2}:V\\times V\\rightarrow \\mathbb{N}\\cup \\{0\\}$, as $d_{G,2}(x,y)=\\min\\{d_G(x,y),2\\},$ where $d_G(x,y)$ is the length of a shortest path between $x$ and $y$ and $\\mathbb{N}$ is the set of positive integers. Then $(V,d_{G,2 })$ is a metric space. We say that a set $S\\subseteq V$ is a $k$-adjacency generator for $G$ if for every two vertices $x,y\\in V$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1501.04647","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"}