%0 Journal Article
%T Bounds on the restrained Roman domination number of a graph
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Abdollahzadeh Ahangar, H.
%A Mirmehdipour, S.R.
%D 2016
%\ 06/01/2016
%V 1
%N 1
%P 75-82
%! Bounds on the restrained Roman domination number of a graph
%K Roman dominating function
%K Roman domination number
%K restrained Roman dominating function
%K restrained Roman domination number
%R 10.22049/cco.2016.13556
%X A {\em Roman dominating function} on a graph $G$ is a function $f:V(G)\rightarrow \{0,1,2\}$ 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 {\em restrained Roman dominating} function $f$ is a Roman dominating function if the vertices with label 0 induce a subgraph with no isolated vertex. The weight of a restrained Roman dominating function is the value $\omega(f)=\sum_{u\in V(G)} f(u)$. The minimum weight of a restrained Roman dominating function of $G$ is called the { \em restrained Roman domination number} of $G$ and denoted by $\gamma_{rR}(G)$. In this paper we establish some sharp bounds for this parameter.
%U https://comb-opt.azaruniv.ac.ir/article_13556_af7da9ddc41c8343edb4835aaab47c2c.pdf