# Radio numbers for generalized prism graphs

Paul Martinez; Juan Ortiz; Maggy Tomova; Cindy Wyels

Discussiones Mathematicae Graph Theory (2011)

- Volume: 31, Issue: 1, page 45-62
- ISSN: 2083-5892

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topPaul Martinez, et al. "Radio numbers for generalized prism graphs." Discussiones Mathematicae Graph Theory 31.1 (2011): 45-62. <http://eudml.org/doc/270953>.

@article{PaulMartinez2011,

abstract = {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.},

author = {Paul Martinez, Juan Ortiz, Maggy Tomova, Cindy Wyels},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {radio number; radio labeling; prism graphs},

language = {eng},

number = {1},

pages = {45-62},

title = {Radio numbers for generalized prism graphs},

url = {http://eudml.org/doc/270953},

volume = {31},

year = {2011},

}

TY - JOUR

AU - Paul Martinez

AU - Juan Ortiz

AU - Maggy Tomova

AU - Cindy Wyels

TI - Radio numbers for generalized prism graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2011

VL - 31

IS - 1

SP - 45

EP - 62

AB - 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.

LA - eng

KW - radio number; radio labeling; prism graphs

UR - http://eudml.org/doc/270953

ER -

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