Journal article
Radio numbers for generalized prism graphs
Discussiones Mathematicae - Graph Theory, Vol.31(1), pp.45-62
2011
DOI: 10.7151/dmgt.1529
Abstract
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 $\{((i,j),(i,j \pm 1))\} \cup \{((1,i),(2,i+\sigma))\,|\,\sigma=-\left\lfloor\frac{s-1}{2}\right\rfloor\,\ldots,0,\ldots,\left\lfloor\frac{s}{2}\right\rfloor\}$. In this paper we determine the radio number of $Z_{n,s}$ for $s=1,2$ and $3$. In the process we develop techniques that are likely to be of use in determining radio numbers of other families of graphs.
Details
- Title: Subtitle
- Radio numbers for generalized prism graphs
- Creators
- Paul MartinezCindy WyelsJuan OrtizMaggy Tomova
- Resource Type
- Journal article
- Publication Details
- Discussiones Mathematicae - Graph Theory, Vol.31(1), pp.45-62
- DOI
- 10.7151/dmgt.1529
- ISSN
- 1234-3099
- eISSN
- 2083-5892
- Language
- English
- Date published
- 2011
- Academic Unit
- Liberal Arts and Science Admin; Mathematics
- Record Identifier
- 9983985988402771
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