- Tytuł:
- The Distance Roman Domination Numbers of Graphs
- Autorzy:
-
Aram, Hamideh
Norouzian, Sepideh
Sheikholeslami, Seyed Mahmoud - Powiązania:
- https://bibliotekanauki.pl/articles/30098151.pdf
- Data publikacji:
- 2013-09-01
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
k-distance Roman dominating function
k-distance Roman domination number
Roman dominating function
Roman domination number - Opis:
- Let $ k $ be a positive integer, and let $ G $ be a simple graph with vertex set $ V (G) $. A k-distance Roman dominating function on $ G $ is a labeling $ f : V (G) → {0, 1, 2} $ such that for every vertex with label 0, there is a vertex with label 2 at distance at most $ k $ from each other. The weight of a $k$-distance Roman dominating function $ f $ is the value $ \omega (f) =∑_{v∈V} f(v) $. The k-distance Roman domination number of a graph $G$, denoted by $\gamma_R^k (D) $, equals the minimum weight of a $k$-distance Roman dominating function on G. Note that the 1-distance Roman domination number $ \gamma_R^1 (G) $ is the usual Roman domination number $ \gamma_R (G) $. In this paper, we investigate properties of the $k$-distance Roman domination number. In particular, we prove that for any connected graph $ G $ of order $ n \geq k +2$, $\gamma_R^k (G) \leq 4n//(2k +3) $ and we characterize all graphs that achieve this bound. Some of our results extend these ones given by Cockayne et al. in 2004 and Chambers et al. in 2009 for the Roman domination number.
- Źródło:
-
Discussiones Mathematicae Graph Theory; 2013, 33, 4; 717-730
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł