Radio numbers for generalized prism graphs
Paul Martinez ; Juan Ortiz ; Maggy Tomova ; Cindy Wyels
Discussiones Mathematicae Graph Theory, Tome 31 (2011), p. 45-62 / Harvested from The Polish Digital Mathematics Library
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A radio labeling is an assignment c:V(G) → N such that every distinct pair of vertices u,v satisfies the inequality d(u,v) + |c(u)-c(v)| ≥ 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 Zn,s, s ≥ 1, n ≥ s, have vertex set (i,j) | i = 1,2 and j = 1,...,n and edge set ((i,j),(i,j ±1)) ∪ ((1,i),(2,i+σ)) | σ = -⌊(s-1)/2⌋...,0,...,⌊s/2⌋. In this paper we determine the radio number of Zn,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.

Publié le : 2011-01-01
EUDML-ID : urn:eudml:doc:270953 
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     title = {Radio numbers for generalized prism graphs},
     journal = {Discussiones Mathematicae Graph Theory},
     volume = {31},
     year = {2011},
     pages = {45-62},
     zbl = {1284.05240},
     language = {en},
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Paul Martinez; Juan Ortiz; Maggy Tomova; Cindy Wyels. Radio numbers for generalized prism graphs. Discussiones Mathematicae Graph Theory, Tome 31 (2011) pp. 45-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1529/

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