Geodesic
Radio numbers for generalized prism graphs
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 1, pp. 45-62

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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 Z_n,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 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.
Keywords: radio number, radio labeling, prism graphs 
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Martinez, Paul; Ortiz, Juan; Tomova, Maggy; Wyels, Cindy. Radio numbers for generalized prism graphs. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 1, pp. 45-62. http://geodesic.mathdoc.fr/item/DMGT_2011_31_1_a3/