Article (Scientific journals)
Constant 2-labellings and an application to (r,a,b)-covering codes
Vandomme, Elise; Gravier, Sylvain
2017In Discussiones Mathematicae. Graph Theory, 37 (4), p. 891-918
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Keywords :
covering codes; weighted codes; infinite grid; vertex-weighted graphs
Abstract :
[en] 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 Z^2 whenever |a−b|>4, r>1 and we give the precise values of a and b. This is a refinement of Axenovich’s theorem proved in 2003.
Disciplines :
Mathematics
Author, co-author :
Vandomme, Elise ;  Université de Liège > Département de mathématique > Mathématiques discrètes
Gravier, Sylvain;  Université de Grenoble > Institut Fourier
Language :
English
Title :
Constant 2-labellings and an application to (r,a,b)-covering codes
Publication date :
2017
Journal title :
Discussiones Mathematicae. Graph Theory
ISSN :
1234-3099
eISSN :
2083-5892
Publisher :
Technical University Press, Poland
Volume :
37
Issue :
4
Pages :
891-918
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 15 June 2017

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