Geodesic
Bounds on the global double Roman domination number in graphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 539-554

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Let G be a simple graph of order n and let γ_gdR(G) be the global double Roman domination number of G. In this paper, we give some upper bounds on the global double Roman domination number of G. In particular, we completely characterize the graph G with γ_gdR(G)=2n-2 and γ_gdR(G)=2n-3. Our results answer a question posed by Shao et al. (2019).
Keywords: global double Roman domination, double Roman domination, complement 
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     title = {Bounds on the global double {Roman} domination number in graphs},
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Hao, Guoliang; Wei, Shouliu; Sheikholeslami, Seyed Mahmoud; Chen, Xiaodan. Bounds on the global double Roman domination number in graphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 2, pp. 539-554. http://geodesic.mathdoc.fr/item/DMGT_2024_44_2_a6/