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The Radio numbers of all graphs of order $n$ and diameter $n-2$
- Publication Year :
- 2012
-
Abstract
- 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 $n-2$.<br />Comment: 21 pages, 10 figures
- Subjects :
- Mathematics - Combinatorics
05C78 (05C15, 05C38)
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1206.6327
- Document Type :
- Working Paper