# Global Roman Domination in Trees

## M. Atapour

### 2014

We present some sharp bounds for global Roman domination number

## Highlights

• The weight of an Roman dominating function is the sum of its function value over all vertices
• We prove that for any tree of order $$n\ge 4$$, $$\gamma _{gR}(T)\le \gamma _{R}(T)+2$$ and we characterize all trees with $$\gamma _{gR}(T)=\gamma _{R}(T)+2$$ and $$\gamma _{gR}(T)= \gamma _{R}(T)+1$$