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Article Dans Une Revue Discussiones Mathematicae Graph Theory Année : 2017

Constant 2-labellings and an application to (r,a,b)-covering codes

Sylvain Gravier

Résumé

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 vertical bar a-b vertical bar > 4, r >= 2 and we give the precise values of a and b. This is a refinement of Axenovich's theorem proved in 2003.

Dates et versions

hal-01993909 , version 1 (25-01-2019)

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Citer

Sylvain Gravier, Elise Vandomme. Constant 2-labellings and an application to (r,a,b)-covering codes. Discussiones Mathematicae Graph Theory, 2017, 37 (4), pp.891-918. ⟨10.7151/dmgt.1973⟩. ⟨hal-01993909⟩
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