- Tytuł:
- Bounds on the Signed Roman k-Domination Number of a Digraph
- Autorzy:
-
Chen, Xiaodan
Hao, Guoliang
Volkmann, Lutz - Powiązania:
- https://bibliotekanauki.pl/articles/31343713.pdf
- Data publikacji:
- 2019-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
signed Roman k-dominating function
signed Roman k-domination number
digraph
oriented tree - Opis:
- Let $k$ be a positive integer. A signed Roman $k$-dominating function (SRkDF) on a digraph $D$ is a function $ f : V (D) \rightarrow \{−1, 1, 2 \} $ satisfying the conditions that (i) $ \Sigma_{ x \in N^− [v] } f(x) \ge k $ for each $ v \in V (D) $, where $ N^− [v] $ is the closed in-neighborhood of $v$, and (ii) each vertex $u$ for which $f(u) = −1$ has an in-neighbor $v$ for which $f(v) = 2$. The weight of an SRkDF $f$ is $ \Sigma_{ v \in V (D) } f(v) $. The signed Roman $k$-domination number $ \gamma_{sR}^k (D) $ of a digraph $D$ is the minimum weight of an SRkDF on $D$. We determine the exact values of the signed Roman $k$-domination number of some special classes of digraphs and establish some bounds on the signed Roman $k$-domination number of general digraphs. In particular, for an oriented tree $T$ of order $n$, we show that $ \gamma_{sR}^2 (T) \ge (n + 3)//2 $, and we characterize the oriented trees achieving this lower bound.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2019, 39, 1; 67-79
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł