- Tytuł:
- Domination numbers in graphs with removed edge or set of edges
- Autorzy:
- Lemańska, Magdalena
- Powiązania:
- https://bibliotekanauki.pl/articles/744295.pdf
- Data publikacji:
- 2005
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
connected domination number
weakly connected domination number
edge removal - Opis:
- It is known that the removal of an edge from a graph G cannot decrease a domination number γ(G) and can increase it by at most one. Thus we can write that γ(G) ≤ γ(G-e) ≤ γ(G)+1 when an arbitrary edge e is removed. Here we present similar inequalities for the weakly connected domination number $γ_w$ and the connected domination number $γ_c$, i.e., we show that $γ_w(G) ≤ γ_w(G-e) ≤ γ_w(G)+1$ and $γ_c(G) ≤ γ_c(G-e) ≤ γ_c(G) + 2$ if G and G-e are connected. Additionally we show that $γ_w(G) ≤ γ_w(G-Eₚ) ≤ γ_w(G) + p - 1$ and $γ_c(G) ≤ γ_c(G -Eₚ) ≤ γ_c(G) + 2p - 2$ if G and G - Eₚ are connected and Eₚ = E(Hₚ) where Hₚ of order p is a connected subgraph of G.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 51-56
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł