2012/06/27 by Katherine Benson, Katherine F. Benson, Matthew Porter +4
Computer Science · Engineering · Mathematics · #05C38) #05C78 (05C15 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #graph theory and CDMA systems #math.CO #msc:05C78
paper · pdf · doi:10.48550/arxiv.1206.6327
21 pages, 10 figures
arxiv created 2012/06/27 · openalex publication_date 2012/06/27 · arxiv updated 2012/06/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A radio labeling of a connected graph G is a function c:V(G) → \mathbb Z+ such that for every two distinct vertices u and v of G distance(u,v)+|c(u)-c(v)|≥ 1+ diameter(G). The radio number of a graph G is the smallest integer M for which there exists a labeling c with c(v)≤ M for all v∈ V(G). The radio number of graphs of order n and diameter n-1, i.e., paths, was determined in \citepaths. Here we determine the radio numbers of all graphs of order n and diameter n-2.