Double Roman Domination in Digraphs

  • Guoliang Hao
  • Xiaodan ChenEmail author
  • Lutz Volkmann


Let D be a finite and simple digraph with vertex set V(D). A double Roman dominating function (DRDF) on a digraph D is a function \(f:V(D)\rightarrow \{0,1,2,3\}\) satisfying the condition that if \(f(v)=0\), then the vertex v must have at least two in-neighbors assigned 2 under f or one in-neighbor assigned 3, while if \(f(v)=1\), then the vertex v must have at least one in-neighbor assigned 2 or 3. The weight of a DRDF f is the sum \(\sum _{v\in V(D)}f(v)\). The double Roman domination number of a digraph D is the minimum weight of a DRDF on D. In this paper, we initiate the study of the double Roman domination of digraphs, and we give several relations between the double Roman domination number of a digraph and other domination parameters such as Roman domination number, k-domination number and signed domination number. Moreover, various bounds on the double Roman domination number of a digraph are presented, and a Nordhaus–Gaddum type inequality for the parameter is also given.


Double Roman domination Roman domination k-domination Signed domination Digraph Nordhaus–Gaddum 

Mathematics Subject Classification

05C20 05C69 



The first author was supported by the Research Foundation of Education Bureau of Jiangxi Province of China (No. GJJ150561) and the Doctor Fund of East China University of Technology (No. DHBK2015319). The second author was supported partially by National Natural Science Foundation of China (No. 11501133) and Guangxi Natural Science Foundation (Nos. 2014GXNSFBA118008, 2016GXNSFAA380293).


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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

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.Lehrstuhl II für MathematikRWTH Aachen UniversityAachenGermany

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