@article {
author = {Pushpam, Roushini and Padmapriea, Sampath},
title = {Restrained roman domination in graphs},
journal = {Transactions on Combinatorics},
volume = {4},
number = {1},
pages = {1-17},
year = {2015},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2015.4395},
abstract = {A \textit{Roman dominating function} (RDF) on a graph $G = (V,E)$ is defined to be a function $ f:V \rightarrow \lbrace 0,1,2\rbrace$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A set $S \subseteq V$ is a \textit{Restrained dominating set} if every vertex not in $S$ is adjacent to a vertex in $S$ and to a vertex in $V - S$. We define a \textit{Restrained Roman dominating function} on a graph $G = (V,E)$ to be a function $f : V \rightarrow \lbrace 0,1,2 \rbrace$ satisfying the condition that every vertex $u$ for which $f(u) = 0 $ is adjacent to at least one vertex $v$ for which $f(v)=2$ and at least one vertex $w$ for which $f(w) = 0$. The \textit{weight} of a Restrained Roman dominating function is the value $f(V)= \sum _{u \in V} f(u)$. The minimum weight of a Restrained Roman dominating function on a graph $G$ is called the Restrained Roman domination number of $G$ and denoted by $\gamma_{rR}(G)$. In this paper, we initiate a study of this parameter.},
keywords = {domination,Roman domination,Restrained domination},
url = {https://toc.ui.ac.ir/article_4395.html},
eprint = {https://toc.ui.ac.ir/article_4395_4464d5648abc97e1c5cf12df1d49d67c.pdf}
}