- Tytuł:
- The Signed Total Roman k-Domatic Number Of A Graph
- Autorzy:
- Volkmann, Lutz
- Powiązania:
- https://bibliotekanauki.pl/articles/31341581.pdf
- Data publikacji:
- 2017-11-27
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
signed total Roman k-dominating function
signed total Roman k-domination number
signed total Roman k-domatic number - Opis:
- Let $ k \ge 1 $ be an integer. A signed total Roman $k$-dominating function on a graph $G$ is a function $ f : V (G) \rightarrow {−1, 1, 2} $ such that $ \Sigma_{ u \in N(v) } f(u) \ge k $ for every $ v \in V (G) $, where $ N(v) $ is the neighborhood of $ v $, and every vertex $ u \in V (G) $ for which $ f(u) = −1 $ is adjacent to at least one vertex w for which $ f(w) = 2 $. A set $ { f_1, f_2, . . ., f_d} $ of distinct signed total Roman $k$-dominating functions on $G$ with the property that $ \Sigma_{i=1}^d f_i(v) \le k $ for each $ v \in V (G) $, is called a signed total Roman $k$-dominating family (of functions) on $G$. The maximum number of functions in a signed total Roman $k$-dominating family on $G$ is the signed total Roman $k$-domatic number of $G$, denoted by $ d_{stR}^k (G) $. In this paper we initiate the study of signed total Roman $k$-domatic numbers in graphs, and we present sharp bounds for $ d_{stR}^k (G) $. In particular, we derive some Nordhaus-Gaddum type inequalities. In addition, we determine the signed total Roman $k$-domatic number of some graphs.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2017, 37, 4; 1027-1038
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł