- Tytuł:
- Signed Total Roman Domination in Digraphs
- Autorzy:
- Volkmann, Lutz
- Powiązania:
- https://bibliotekanauki.pl/articles/31342127.pdf
- Data publikacji:
- 2017-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
digraph
signed total Roman dominating function
signed total Roman domination number - Opis:
- Let $D$ be a finite and simple digraph with vertex set $V (D)$. A signed total Roman dominating function (STRDF) 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 1 $ for each $ v \in V (D) $, where $ N^− (v) $ consists of all vertices of $D$ from which arcs go into $v$, and (ii) every vertex u for which $f(u) = −1$ has an inner neighbor $v$ for which $f(v) = 2$. The weight of an STRDF $f$ is $ w(f) = \Sigma_{ v \in V } (D) f(v) $. The signed total Roman domination number $ \gamma_{stR} (D) $ of $D$ is the minimum weight of an STRDF on $D$. In this paper we initiate the study of the signed total Roman domination number of digraphs, and we present different bounds on $ \gamma_{stR} (D) $. In addition, we determine the signed total Roman domination number of some classes of digraphs. Some of our results are extensions of known properties of the signed total Roman domination number $ \gamma_{stR} (G)$ of graphs $G$.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2017, 37, 1; 261-272
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł