Reference : Constant 2-labellings and an application to (r,a,b)-covering codes
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Constant 2-labellings and an application to (r,a,b)-covering codes
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)
[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.

File(s) associated to this reference

Fulltext file(s):

Open access
DMGT_Gravier_Vandomme.pdfPublisher postprint318.47 kBView/Open

Bookmark and Share SFX Query

All documents in ORBi are protected by a user license.