We present some sharp bounds for global Roman domination number

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- 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 \(\gamma _{gR}(T)= \gamma _{R}(T)+1\)

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