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On the Global Double Roman Domination of Graphs

  • Guoliang Hao
  • Xiaodan ChenEmail author
Article
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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).

Keywords

Global double Roman domination number Double Roman domination number Tree 

Mathematics Subject Classification

05C69 

Notes

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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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2019

Authors and Affiliations

  1. 1.College of ScienceEast China University of TechnologyNanchangPeople’s Republic of China
  2. 2.College of Mathematics and Information ScienceGuangxi UniversityNanningPeople’s Republic of China
  3. 3.Guangxi Center for Mathematical ResearchGuangxi UniversityNanningPeople’s Republic of China

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