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

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Gravier S., Vandomme È.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 4

891-918

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Gravier S.

1 Vandomme È.

1 2017

Wyniki wyszukiwania

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