- Tytuł:
- On distinguishing and distinguishing chromatic numbers of hypercubes
- Autorzy:
- Klöckl, Werner
- Powiązania:
- https://bibliotekanauki.pl/articles/743050.pdf
- Data publikacji:
- 2008
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
distinguishing number
distinguishing chromatic number
hypercube
weak Cartesian product - Opis:
-
The distinguishing number D(G) of a graph G is the least integer d such that G has a labeling with d colors that is not preserved by any nontrivial automorphism. The restriction to proper labelings leads to the definition of the distinguishing chromatic number $χ_D(G)$ of G.
Extending these concepts to infinite graphs we prove that $D(Q_ℵ₀) = 2$ and $χ_D(Q_ℵ₀) = 3$, where $Q_ℵ₀$ denotes the hypercube of countable dimension. We also show that $χ_D(Q₄) = 4$, thereby completing the investigation of finite hypercubes with respect to $χ_D$.
Our results extend work on finite graphs by Bogstad and Cowen on the distinguishing number and Choi, Hartke and Kaul on the distinguishing chromatic number. - Źródło:
-
Discussiones Mathematicae Graph Theory; 2008, 28, 3; 419-429
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł