Double Roman Domination in Digraphs

作者：Hao, Guoliang; Chen, Xiaodan^*; Volkmann, Lutz

来源：Bulletin of the Malaysian Mathematical Sciences Society, 2019, 42(5): 1907-1920.

DOI：10.1007/s40840-017-0582-9

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

Let D be a finite and simple digraph with vertex set V(D). A double Roman dominating DRDF) on a digraph D is a function f:V(D)->{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 Sigma v is an element of 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.

• 出版日期2019-9
• 单位东华理工大学; 广西大学