- Tytuł:
- Secure domination and secure total domination in graphs
- Autorzy:
-
Klostermeyer, William
Mynhardt, Christina - Powiązania:
- https://bibliotekanauki.pl/articles/743322.pdf
- Data publikacji:
- 2008
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
secure domination
total domination
secure total domination
clique covering - Opis:
- A secure (total) dominating set of a graph G = (V,E) is a (total) dominating set X ⊆ V with the property that for each u ∈ V-X, there exists x ∈ X adjacent to u such that $(X-{x}) ∪ {u}$ is (total) dominating. The smallest cardinality of a secure (total) dominating set is the secure (total) domination number $γ_s(G)(γ_{st}(G))$. We characterize graphs with equal total and secure total domination numbers. We show that if G has minimum degree at least two, then $γ_{st}(G) ≤ γ_s(G)$. We also show that $γ_{st}(G)$ is at most twice the clique covering number of G, and less than three times the independence number. With the exception of the independence number bound, these bounds are sharp.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2008, 28, 2; 267-284
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł