Abstract
We establish some inequalities between the global double Roman domination number \(\gamma _\mathrm{gdR}(G)\) and double Roman domination number \(\gamma _\mathrm{dR}(G)\) of graphs G. We also completely characterize the trees T with \(\gamma _\mathrm{gdR}(T)=\gamma _\mathrm{dR}(T)+k\) for \(k\in \{0,1,2,3\}\), which partially answer an open problem posed by Shao et al. (J Discrete Math Sci Cryptogr 22:31–44, 2019).
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Acknowledgements
The authors would like to thank the anonymous referees for their valuable comments and suggestions which have contributed to the final preparation of the paper. This study was supported by NSFC (Nos. 11861011, 11501133), the Research Foundation of Education Bureau of Jiangxi Province of China (No. GJJ180374) and the Doctor Fund of East China University of Technology (No. DHBK2015319).
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Communicated by Xueliang Li.
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Hao, G., Chen, X. On the Global Double Roman Domination of Graphs. Bull. Malays. Math. Sci. Soc. 43, 3007–3018 (2020). https://doi.org/10.1007/s40840-019-00851-4
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DOI: https://doi.org/10.1007/s40840-019-00851-4