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

Sylvain Gravier; Èlise Vandomme

Discussiones Mathematicae Graph Theory (2017)

- Volume: 37, Issue: 4, page 891-918
- ISSN: 2083-5892

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topSylvain 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 -

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