{"paper":{"title":"Radio numbers for generalized prism graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Cindy Wyels, Juan Ortiz, Maggy Tomova, Paul Martinez","submitted_at":"2010-07-29T22:53:08Z","abstract_excerpt":"A radio labeling is an assignment $c:V(G) \\rightarrow \\textbf{N}$ such that every distinct pair of vertices $u,v$ satisfies the inequality $d(u,v)+|c(u)-c(v)|\\geq \\diam(G)+1$. The span of a radio labeling is the maximum value. The radio number of $G$, $rn(G)$, is the minimum span over all radio labelings of $G$. Generalized prism graphs, denoted $Z_{n,s}$, $s \\geq 1$, $n\\geq s$, have vertex set $\\{(i,j)\\,|\\, i=1,2 \\text{and} j=1,...,n\\}$ and edge set $\\{((i,j),(i,j \\pm 1))\\} \\cup \\{((1,i),(2,i+\\sigma))\\,|\\,\\sigma=-\\left\\lfloor\\frac{s-1}{2}\\right\\rfloor\\,\\ldots,0,\\ldots,\\left\\lfloor\\frac{s}{2}\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.5346","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"}