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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 $x,y\\in V$"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1501.04647","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-01-19T21:22:50Z","cross_cats_sorted":[],"title_canon_sha256":"6d86a4b3db9fee80e4010d0dd027ad8c1d91139c7722f1657cddc946e336ff0e","abstract_canon_sha256":"b3dfd94efa5c12816a0c606035480f33696c5b8b38a0bdc0a5ba2c8131128e37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:46.598504Z","signature_b64":"my+DXgG/a+G2h9guW2MCXJBI2DkXUDER6MbIZOXb40f3BCDQ//yTd80uxN+F8Hxjj+v70bpj7/yjj4G6B35BBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa7866d830a08ed7c0f9711b3909e3dc37d9f09a96e3783cbf34772966b4ed7e","last_reissued_at":"2026-05-18T01:29:46.597919Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:46.597919Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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. 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