﻿ Total double Roman domination in graphs

# Total double Roman domination in graphs

نویسندگان

• Guoliang Hao College of Science, East China University of Technology, Nanchang, P. R. China

چکیده

Let \$G\$ be a simple graph with vertex set \$V\$. A double Roman dominating function (DRDF) on \$G\$ is a function \$f:Vrightarrow{0,1,2,3}\$ satisfying that if \$f(v)=0\$, then the vertex \$v\$ must be adjacent to at least two vertices assigned \$2\$ or one vertex assigned \$3\$ under \$f\$, whereas if \$f(v)=1\$, then the vertex \$v\$ must be adjacent to at least one vertex assigned \$2\$ or \$3\$. The weight of a DRDF \$f\$ is the sum \$sum_{vin V}f(v)\$. A total double Roman dominating function (TDRDF) on a graph \$G\$ with no isolated vertex is a DRDF \$f\$ on \$G\$ with the additional property that the subgraph of \$G\$ induced by the set \${vin V:f(v)ne0}\$ has no isolated vertices. The total double Roman domination number \$gamma_{tdR}(G)\$ is the minimum weight of a TDRDF on \$G\$. In this paper, we give several relations between the total double Roman domination number of a graph and other domination parameters and we determine the total double Roman domination number of some classes of graphs. برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

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