- Tytuł:
- Signed Roman Edge k -Domination in Graphs
- Autorzy:
-
Asgharsharghi, Leila
Sheikholeslami, Seyed Mahmoud
Volkmann, Lutz - Powiązania:
- https://bibliotekanauki.pl/articles/31342188.pdf
- Data publikacji:
- 2017-02-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
signed Roman edge k -dominating function
signed Roman edge k -domination number - Opis:
- Let $ k \ge 1 $ be an integer, and $ G = (V, E) $ be a finite and simple graph. The closed neighborhood $ N_G [e]$ of an edge $e$ in a graph $G$ is the set consisting of $e$ and all edges having a common end-vertex with $e$. A signed Roman edge $k$-dominating function (SREkDF) on a graph $G$ is a function $ f : E \rightarrow {−1, 1, 2} $ satisfying the conditions that (i) for every edge $e$ of $G$, $ \Sigma_{ x \in N_G [e] } f(x) \ge k $ and (ii) every edge e for which $f(e) = −1$ is adjacent to at least one edge $ e^′ $ for which $ f(e^′) = 2 $. The minimum of the values $ \Sigma_{e \in E} f(e) $, taken over all signed Roman edge $k$-dominating functions $f$ of $G$ is called the signed Roman edge $k$-domination number of $G$, and is denoted by $ \gamma_{sRk}^' (G) $. In this paper we initiate the study of the signed Roman edge $k$-domination in graphs and present some (sharp) bounds for this parameter.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2017, 37, 1; 39-53
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł