Abdollahzadeh Ahangar, H., Mirmehdipour, S. (2016). Bounds on the restrained Roman domination number of a graph. Communications in Combinatorics and Optimization, 1(1), 75-82. doi: 10.22049/cco.2016.13556

H. Abdollahzadeh Ahangar; S.R. Mirmehdipour. "Bounds on the restrained Roman domination number of a graph". Communications in Combinatorics and Optimization, 1, 1, 2016, 75-82. doi: 10.22049/cco.2016.13556

Abdollahzadeh Ahangar, H., Mirmehdipour, S. (2016). 'Bounds on the restrained Roman domination number of a graph', Communications in Combinatorics and Optimization, 1(1), pp. 75-82. doi: 10.22049/cco.2016.13556

Abdollahzadeh Ahangar, H., Mirmehdipour, S. Bounds on the restrained Roman domination number of a graph. Communications in Combinatorics and Optimization, 2016; 1(1): 75-82. doi: 10.22049/cco.2016.13556

Bounds on the restrained Roman domination number of a graph

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 $f(v) =2$. {color{blue}A {em restrained Roman dominating} function} $f$ is a {color{blue} 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 $omega(f)=sum_{uin V(G)} f(u)$. 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.