The 2-Rainbow Domination of Sierpiński Graphs and Extended Sierpiński Graphs

2017 ◽  
Vol 61 (3) ◽  
pp. 893-906 ◽  
Author(s):  
Jia-Jie Liu ◽  
Shun-Chieh Chang ◽  
Chiou-Jiun Lin
Keyword(s):  
Sierpiński Graphs ◽  
Extended Sierpiński Graphs ◽  
Rainbow Domination

On 2-Rainbow Domination of some Families of Graphs

2011 ◽  
Vol 1 (1) ◽  
pp. 47 ◽  
Author(s):  
Mohammad Tariq Rahim ◽  
M. Ali ◽  
M. Zeb ◽  
G. Ali
Keyword(s):  
Rainbow Domination

scholarly journals Rainbow domination numbers on graphs with given radius

2014 ◽  
Vol 166 ◽  
pp. 115-122 ◽  
Author(s):  
Shinya Fujita ◽  
Michitaka Furuya
Keyword(s):  
Rainbow Domination ◽  
Domination Numbers

On 2-rainbow domination in generalized Petersen graphs

2017 ◽  
Vol 2 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Kuo-Hua Wu ◽  
Yue-Li Wang ◽  
Chiun-Chieh Hsu ◽  
Chao-Cheng Shih
Keyword(s):  
Generalized Petersen Graphs ◽  
Rainbow Domination ◽  
Petersen Graphs

scholarly journals On k-rainbow domination in middle graphs

2021 ◽  
Author(s):  
Kijung Kim
Keyword(s):  
Minimum Weight ◽  
Domination Number ◽  
Simple Graph ◽  
Upper And Lower Bounds ◽  
Matching Number ◽  
Domatic Number ◽  
Rainbow Domination ◽  
Vertex Set ◽  
Middle Graph ◽  
Dominating Function

Let $G$ be a finite simple graph with vertex set $V(G)$ and edge set $E(G)$. A function $f : V(G) \rightarrow \mathcal{P}(\{1, 2, \dotsc, k\})$ is a \textit{$k$-rainbow dominating function} on $G$ if for each vertex $v \in V(G)$ for which $f(v)= \emptyset$, it holds that $\bigcup_{u \in N(v)}f(u) = \{1, 2, \dotsc, k\}$. The weight of a $k$-rainbow dominating function is the value $\sum_{v \in V(G)}|f(v)|$. The \textit{$k$-rainbow domination number} $\gamma_{rk}(G)$ is the minimum weight of a $k$-rainbow dominating function on $G$. In this paper, we initiate the study of $k$-rainbow domination numbers in middle graphs. We define the concept of a middle $k$-rainbow dominating function, obtain some bounds related to it and determine the middle $3$-rainbow domination number of some classes of graphs. We also provide upper and lower bounds for the middle $3$-rainbow domination number of trees in terms of the matching number. In addition, we determine the $3$-rainbow domatic number for the middle graph of paths and cycles.

scholarly journals Outer-independent k-rainbow domination

2019 ◽  
Vol 13 (1) ◽  
pp. 883-891 ◽  
Author(s):  
Qiong Kang ◽  
Vladimir Samodivkin ◽  
Zehui Shao ◽  
Seyed Mahmoud Sheikholeslami ◽  
Marzieh Soroudi
Keyword(s):  
Rainbow Domination
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