University of IsfahanTransactions on Combinatorics2251-86574120150301Restrained roman domination in graphs117439510.22108/toc.2015.4395ENRoushini LeelyPushpamDepartment of Mathematics
D.B.Jain College,
Chennai 97
IndiaSampathPadmaprieaDepartment of Mathematics
Sri Sairam Engineering College
Chennai 44
IndiaJournal Article20130917A textit{Roman dominating function} (RDF) on a graph $G = (V,E)$ is defined to be a function $ f:V rightarrow lbrace 0,1,2rbrace$ 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 <em>Restrained Roman domination number</em> of $G$ and denoted by $gamma_{rR}(G)$. In this paper, we initiate a study of this parameter.https://toc.ui.ac.ir/article_4395_4464d5648abc97e1c5cf12df1d49d67c.pdf