- Tytuł:
- Domination parameters of a graph with added vertex
- Autorzy:
- Zwierzchowski, M.
- Powiązania:
- https://bibliotekanauki.pl/articles/2050876.pdf
- Data publikacji:
- 2004
- Wydawca:
- Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
- Tematy:
-
total domination number
strong domination number
subdivision - Opis:
- Let $G = (V, E)$ be a graph. A subset $D \subseteq V$ is a total dominating set of $G$ if for every vertex $y \in V$ there is a vertex $x \in D$ with $xy \in E$. A subset $D \subseteq V$ is a strong dominating set of G if for every vertex $y \in V - D$ there is a vertex $x \in D$ with $xy \in E and deg_{G}(x) \geq deg_{G}(y)$. The total domination number $\gamma_{t}(G)$ (the strong domination number $\gamma_{S}(G)$) is defined as the minimum cardinality of a total dominating set (a strong dominating set) of $G$. The concept of total domination was first defined by Cockayne, Dawes and Hedetniemi in 1980 [1], while the strong domination was introduced by Sampathkumar and Pushpa Latha in 1996 [3]. By a subdivision of an edge $uv \in E$ we mean removing edge $uv$, adding a new vertex $x$, and adding edges $ux$ and $vx$. A graph obtained from $G$ by subdivision an edge $uv \in E$ is denoted by $G \oplus uxvx$. The behaviour of the total domination number and the strong domination number of a graph $G \oplus u_{x}v_{x}$ is developed.
- Źródło:
-
Opuscula Mathematica; 2004, 24, 2; 231-234
1232-9274
2300-6919 - Pojawia się w:
- Opuscula Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł