- Tytuł:
- Characterizing Cartesian fixers and multipliers
- Autorzy:
-
Benecke, Stephen
Mynhardt, Christina - Powiązania:
- https://bibliotekanauki.pl/articles/743719.pdf
- Data publikacji:
- 2012
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
Cartesian product
prism fixer
Cartesian fixer
prism doubler
Cartesian multiplier
domination number - Opis:
-
Let G ☐ H denote the Cartesian product of the graphs G and H. In 2004, Hartnell and Rall [On dominating the Cartesian product of a graph and K₂, Discuss. Math. Graph Theory 24(3) (2004), 389-402] characterized prism fixers, i.e., graphs G for which γ(G ☐ K₂) = γ(G), and noted that γ(G ☐ Kₙ) ≥ min{|V(G)|, γ(G)+n-2}. We call a graph G a consistent fixer if γ(G ☐ Kₙ) = γ(G)+n-2 for each n such that 2 ≤ n < |V(G)|- γ(G)+2, and characterize this class of graphs.
Also in 2004, Burger, Mynhardt and Weakley [On the domination number of prisms of graphs, Dicuss. Math. Graph Theory 24(2) (2004), 303-318] characterized prism doublers, i.e., graphs G for which γ(G ☐ K₂) = 2γ(G). In general γ(G ☐ Kₙ) ≤ nγ(G) for any n ≥ 2. We call a graph attaining equality in this bound a Cartesian n-multiplier and also characterize this class of graphs. - Źródło:
-
Discussiones Mathematicae Graph Theory; 2012, 32, 1; 161-175
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł