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Title:
Bounds on the global double Roman domination number in graphs
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Discussiones Mathematicae Graph Theory 44(2) (2024) 539-554
Received: 2021-12-03 , Revised: 2022-04-23 , Accepted: 2022-04-23 , Available online: 2022-05-25 , https://doi.org/10.7151/dmgt.2460
Abstract:
Let $G$ be a simple graph of order $n$ and let $\gamma_{gdR}(G)$ 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 $\gamma_{gdR}(G)=2n-2$ and
$\gamma_{gdR}(G)=2n-3$. Our results answer a question posed by Shao
et al. (2019).
Keywords:
global double Roman domination, double Roman domination, complement
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