Radio k-labelings for Cartesian products of graphs

@article{MustaphaKchikech2008,
abstract = {Frequency planning consists in allocating frequencies to the transmitters of a cellular network so as to ensure that no pair of transmitters interfere. We study the problem of reducing interference by modeling this by a radio k-labeling problem on graphs: For a graph G and an integer k ≥ 1, a radio k-labeling of G is an assignment f of non negative integers to the vertices of G such that $|f(x)-f(y)| ≥ k+1-d_G(x,y)$, for any two vertices x and y, where $d_G(x,y)$ is the distance between x and y in G. The radio k-chromatic number is the minimum of maxf(x)-f(y):x,y ∈ V(G) over all radio k-labelings f of G. In this paper we present the radio k-labeling for the Cartesian product of two graphs, providing upper bounds on the radio k-chromatic number for this product. These results help to determine upper and lower bounds for radio k-chromatic numbers of hypercubes and grids. In particular, we show that the ratio of upper and lower bounds of the radio number and the radio antipodal number of the square grid is asymptotically [3/2].},
author = {Mustapha Kchikech, Riadh Khennoufa, Olivier Togni},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {graph theory; radio channel assignment; radio k-labeling; Cartesian product; radio number; antipodal number; radio -labeling},
language = {eng},
number = {1},
pages = {165-178},
title = {Radio k-labelings for Cartesian products of graphs},
url = {http://eudml.org/doc/270576},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Mustapha Kchikech
AU - Riadh Khennoufa
AU - Olivier Togni
TI - Radio k-labelings for Cartesian products of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2008
VL - 28
IS - 1
SP - 165
EP - 178
AB - Frequency planning consists in allocating frequencies to the transmitters of a cellular network so as to ensure that no pair of transmitters interfere. We study the problem of reducing interference by modeling this by a radio k-labeling problem on graphs: For a graph G and an integer k ≥ 1, a radio k-labeling of G is an assignment f of non negative integers to the vertices of G such that $|f(x)-f(y)| ≥ k+1-d_G(x,y)$, for any two vertices x and y, where $d_G(x,y)$ is the distance between x and y in G. The radio k-chromatic number is the minimum of maxf(x)-f(y):x,y ∈ V(G) over all radio k-labelings f of G. In this paper we present the radio k-labeling for the Cartesian product of two graphs, providing upper bounds on the radio k-chromatic number for this product. These results help to determine upper and lower bounds for radio k-chromatic numbers of hypercubes and grids. In particular, we show that the ratio of upper and lower bounds of the radio number and the radio antipodal number of the square grid is asymptotically [3/2].
LA - eng
KW - graph theory; radio channel assignment; radio k-labeling; Cartesian product; radio number; antipodal number; radio -labeling
UR - http://eudml.org/doc/270576
ER -