{"paper":{"title":"The Radio numbers of all graphs of order $n$ and diameter $n-2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Katherine Benson, Maggy Tomova, Matthew Porter","submitted_at":"2012-06-27T16:23:43Z","abstract_excerpt":"A radio labeling of a connected graph $G$ is a function $c:V(G) \\to \\mathbb Z_+$ such that for every two distinct vertices $u$ and $v$ of $G$ $$\\text{distance}(u,v)+|c(u)-c(v)|\\geq 1+ \\text{diameter}(G).$$ The radio number of a graph $G$ is the smallest integer $M$ for which there exists a labeling $c$ with $c(v)\\leq M$ for all $v\\in V(G)$. The radio number of graphs of order $n$ and diameter $n-1$, i.e., paths, was determined in \\cite{paths}. Here we determine the radio numbers of all graphs of order $n$ and diameter $n-2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.6327","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"}