Reference : Constant 2-labellings and an application to (r,a,b)-covering codes
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/2268/211860
Constant 2-labellings and an application to (r,a,b)-covering codes
English
Vandomme, Elise mailto [Université de Liège > Département de mathématique > Mathématiques discrètes >]
Gravier, Sylvain [Université de Grenoble > Institut Fourier > > >]
In press
Discussiones Mathematicae Graph Theory
Yes (verified by ORBi)
International
1234-3099
2083-5892
[en] covering codes ; weighted codes ; infinite grid ; vertex-weighted graphs
[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.
Researchers
http://hdl.handle.net/2268/211860
10.7151/dmgt
http://www.discuss.wmie.uz.zgora.pl/gt/

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