Constant 2-Labellings And An Application To (R, A, B)-Covering Codes

Sylvain Gravier, and Èlise Vandomme. "Constant 2-Labellings And An Application To (R, A, B)-Covering Codes." Discussiones Mathematicae Graph Theory 37.4 (2017): 891-918. <http://eudml.org/doc/288508>.

@article{SylvainGravier2017,
abstract = {We introduce the concept of constant 2-labelling of a vertex-weighted graph and show how it can be used to obtain perfect weighted coverings. Roughly speaking, a constant 2-labelling of a vertex-weighted graph is a black and white colouring of its vertex set which preserves the sum of the weights of black vertices under some automorphisms. We study constant 2-labellings on four types of vertex-weighted cycles. Our results on cycles allow us to determine (r, a, b)-codes in Z2 whenever |a − b| > 4, r ≥ 2 and we give the precise values of a and b. This is a refinement of Axenovich’s theorem proved in 2003.},
author = {Sylvain Gravier, Èlise Vandomme},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {covering codes; weighted codes; infinite grid; vertex-weighted graphs.},
language = {eng},
number = {4},
pages = {891-918},
title = {Constant 2-Labellings And An Application To (R, A, B)-Covering Codes},
url = {http://eudml.org/doc/288508},
volume = {37},
year = {2017},
}

TY - JOUR
AU - Sylvain Gravier
AU - Èlise Vandomme
TI - Constant 2-Labellings And An Application To (R, A, B)-Covering Codes
JO - Discussiones Mathematicae Graph Theory
PY - 2017
VL - 37
IS - 4
SP - 891
EP - 918
AB - We introduce the concept of constant 2-labelling of a vertex-weighted graph and show how it can be used to obtain perfect weighted coverings. Roughly speaking, a constant 2-labelling of a vertex-weighted graph is a black and white colouring of its vertex set which preserves the sum of the weights of black vertices under some automorphisms. We study constant 2-labellings on four types of vertex-weighted cycles. Our results on cycles allow us to determine (r, a, b)-codes in Z2 whenever |a − b| > 4, r ≥ 2 and we give the precise values of a and b. This is a refinement of Axenovich’s theorem proved in 2003.
LA - eng
KW - covering codes; weighted codes; infinite grid; vertex-weighted graphs.
UR - http://eudml.org/doc/288508
ER -