{"paper":{"title":"Fault-Tolerant Metric Dimension of $P(n,2)$ with Prism Graph","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A. Q. Baig, M. Naeem, M. O. Ahmad, Z. Ahmad","submitted_at":"2018-11-14T05:59:36Z","abstract_excerpt":"Let $G$ be a connected graph and $d(a,b)$ be the distance between the vertices $a$ and $b$. A subset $U =\\{u_1,u_2,\\cdots,u_k\\}$ of the vertices is called a resolving set for $G$ if for every two distinct vertices $a,b \\in V(G)$, there is a vertex $u_\\xi \\in U$ such that $d(a,u_\\xi)\\neq d(b,u_\\xi)$. A resolving set containing a minimum number of vertices is called a metric basis for $G$ and the number of vertices in a metric basis is its metric dimension denoted by $dim(G)$. A resolving set $U$ for $G$ is fault-tolerant if $U \\setminus \\{u\\}$ is also a resolving set, for each $u \\in U$, and th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.05973","kind":"arxiv","version":1},"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"}