- Tytuł:
- Constant 2-Labellings And An Application To (R, A, B)-Covering Codes
- Autorzy:
-
Gravier, Sylvain
Vandomme, Èlise - Powiązania:
- https://bibliotekanauki.pl/articles/31341603.pdf
- Data publikacji:
- 2017-11-27
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
covering codes
weighted codes
infinite grid
vertex-weighted graphs - Opis:
- 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 $ \mathbb{Z}^2 $ 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.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2017, 37, 4; 891-918
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł